i'd be worried about double stick tape underneath. my boards are pretty heavy. with the router weight on top and the weight of the board, I'm thinking the board could come loose under the router.C'man's idea would surround the cutting board. The board would rest in the middle and temporarily affixed to the surface, e.g. with a couple of pieces of double sided tape. The jig would be clamped in place.
The router would be place on the board, with the base against the jig, and the bit plunged into the board.
The circular part of the base would be kept against the jig as the router is moved along each side of the jig.
The jig would be adjusted as needed for the router bit to trace the desired channel, e.g., 3/4in - 1in inside the circumference of the board.