Try this on scrap:
1. Set the grooving plane for a very light cut.
2. Use a gauge to run lines along the end grain exactly where the grooving plane will go.
3. Very carefully, run the grooving plane for a pass, watching very carefully to make sure you aren’t going outside the gauge lines, etc. You are just trying to get a little bit down into the material.
4. The previous step has left a tiny shoulder defining the groove. Take your tenon saw and run it along that groove, working along the length to get part way down to your depth. Do both sides.
5. Return to the grooving plane to remove the material between the saw kerfs.
6. Light passes with a sharp bench plane when you are all done might tidy things up.

A wide edge like that isn’t going to be easy to run a tenon saw in, so be patient. Make sure your initial groove is deep enough to set the saw. It might take a couple passes with the gauge, plow, back to gauge to feel confident. You may be tempted to use a knife to strengthen that gauge line, but take care. It can work, but it can also slip out and put a cut into the end grain. Also that “clean up with a bench plane” in Step 6 works best when the top line is a perfect as possible, which happens most easily right off the gauge.

Lubricate the plow blade, fence, skate.

If you push the plow all the way through and off the edge, you will break out the grain at the end. You may need to handle that last portion with a chisel. Hope that makes sense. It’s been awhile since I did one of these.

It may still be a problem. At the very least, when you get down to depth, you can still break off the fibers at that final depth. But, also at the very start, making your first passes, since this is end grain, not just cross grain, and the fibers are standing right on end, when you come across and break out the fibers, it may make a ragged edge in the vertical walls of the groove you plowed in the long grain because the fibers being broken pull out their brothers that they are stuck to. Sort of hard to explain. Whether you do long grain first or not, I’d suggest using a chisel to work the last bit of the groove so that the plow blade will never touch the final corner. You just need a tiny bit. It only takes a second to do. A file is probably fine, too.

This is a good reason for experimenting with scrap. 🙂

I’m sort of hoping that someone else has a magic way of doing this that is simpler.

Which reminds me….once you get below the surface, you may not need the saw kerfs. That’s a good thing to explore. You may only need to get, say, 1/16 to 1/8″ below the surface and then can just run the plow down to depth. Like I said, it has been too long since I did one of these. I don’t remember, and I think it depends upon how cranky the grain is.

Vivien LEGER wrote:

i was expecting to plow ‘from both side’

My inclination is to always work from a single reference surface or edge whenever possible. There is almost always a small discrepancy between the “parallel” faces and always a slight amount of error in getting on center. So, it takes a great deal of fiddling about to get these things perfect. If you must, you must, but in this case a chisel solves the problem and saves a great deal of time. This is an example of what I call, “don’t waste time by using machine methods with hand tools.” Take advantage of their speed. You see, even though it takes a great deal of effort to land exactly on center so that you can come from both sides, it takes very little effort to get close enough to center that the eye _sees_ the detail as being on center. You may not even have to measure at all. On the other hand, if you flip around and come from the other side, the two grooves give a reference for each other and make discrepancies stand out. “Oh, I’ll just reset my grooving plane fence….” Yes, you could do that, but it is, again, another step and you want the grooves to match up all the way around. So, it is best to leave it set and work off of a common surface all the way around.

You mentioned making a transition to hand tools, so I’m offering this bit of philosophy in case it helps. In my opinion, hand tools require a different way of thinking in order to really reap their benefits.

Assuming the top would be around 1.5 m long (to seat six people) and 0.7 m wide, I would fail at planing and sawing the ends if the top were to be secured in the front vise; just because they would either be 6 ft up in the air or the work having to be done vertically.

So, here’s an alternative that would save me from the above:
1. Make the top from three laminates. If the middle one was from form plywood, then there would be two flat surfaces to glue the lower and upper components to. The edges of the plywood would have to be covered by a “mitred frame” sufficiently wide to allow cutting the middle piece down to its final size.
2. With all three parts to same size and carefully laid out, with the bottom on top, drill several holes for dowels, without passing the through the top piece.
3. Cut the centre piece down to its final, reduced, size.
4. Place dowels in the upper board; apply glue to the upper surface of the middle on and put it over the dowels; and then repeat with the bottom board. Clamp down.
5. Flatten the top surface, if required, and perhaps also the bottom one.
6. Inspect and realise that the groove (½”) is too wide, attempt to make a ¼” thick solid wood centre board, and find that getting it acceptably flat might prove too challenging.
7. Admit defeat. Wait for a day without precipitation, and create the groove in a solid piece, using a power router – working outdoors.
(8. Review the design)

Thanks Ed!

Have a writing desk with a breadboard end. Sorry about the poor picture quality, but what the photo tries to show is the sides and ends as a “frame” around the central part of the table top. The frame is 30 mm (1 1/8″), while the central part is perhaps half of that. The inferior face of the frame is chamfered; all in all making the top look less thick.

This design appears to allow for grooves along all edges, that can be planed on the bench. Add a rebate on the inside of the upper face of the frame, and the centre board (having a corresponding rebate to its inferior face) could form a lap joint with the frame.

Not entirely convinced I am able top put something like together, though…