This is pretty much standard stuff with electric routers and templates along the lines sven-olof suggests. But in days gone bye, I have also made things like this with an inexpensive hardware store circle cutter in a drill press. You cut the circle as deep as you want and then use chisels and a hand router to make a nice smooth bottom. If you want to go totally the hand tool route, there are very similar adjustable circle cutters that are used in braces. They are sold on ebay. I have a small one that I got somewhere and have not done much with yet. I do not know how large a circle a larger one can produce but it might be worth looking on ebay to see if there is somethiing that can make your sized circle.