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Does anyone know what these corners are called?
(reddthat.com)
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Since you mention you are researching how to do it properly, the answer is "with a router jig".
A piece of wood with a circle cut in it matching the feature you want. Carefully line it up on your workpiece with 2 additional scraps making a fence referencing the two corner surfaces. Once you have it aligned how you want, screw/glue the fences to lock them onto your template. Make sure they overhang into your cut-out circle so that you can run a template bit through it to trim them tight to the hole. Doing this means they will provide some support to prevent blowout. Now you can align it to the square corner of your board and clamp it on, then quickly copy the feature to all corners using the same template/bearing bit.
Oh damn. I never thought about adding the extra two pieces. That's good. Thanks.
Just to add some extra detail for others. The router bits have bearings that ride on the template. The bearings prevent you from cutting farther into your final piece but cuts everything else out.
I have a small table router. I find that holding the router by hand results in some wobbling and therefore imperfect cuts. Because of that I can't clamp the pieces together. So, I bought some industrial double sided tape that works extremely well.