I'd probably start with laying out the cutout, finding center then use a large Forstner bit to hog out the center. Then some smaller bits in the four corners, then chisels for the rest. I'd probably leave it a little proud then some sandpaper on a block to perfect the sides and corners. But the best way to do this would depend a lot on your tools. If I used a chisel in the corners, i'd sharpen the heck out of it first, and I'd scribe the line so it didn't splinter.
I also might choose to use four guide boards as Harry suggests to rough cut the center opening. Cut the outside dimension with the table saw, then lay four boards close around it to define the opening and use a bottom bearing trim bit to cut the inner opening, and use sandpaper to perfect the opening. This would only work if you have your bit perfectly centered. I'd use a trim router because it's smaller and more manageable. You'd have to place the guide boards so the inside cut was accurate, or a little proud so you can sand it flat.
This is definitely going to depend on what tools you have. Or, take it to a local CNC shop and get it done quick and easy.
Lots of ways to skin this cat.
The more I do, the less I accomplish.