Here's the process I used.
  1. Frame the wall witth 2x4 studs leaving space for the holes.

  2. Cut particle board so it exactly fit the wall,on both sides, but don't neail it in place.

  3. Lay the wall boards down flat on top of each other and nail them together so they can't slip.

  4. Locate the centers of the circles and use a compas to draw the circles.

  5. Saw the circles out through both boards. Use a rasp to smooth the cut

  6. Nail up the wall boards.

  7. Set a saw to the right angle to bevel 2x4 blocks so they fit the radius without significant gaps. Saw the blocks.

  8. Saw small 2.4 blocks. In a fixture (for evenness), nail them to the bottom of each beveled block.

  9. Arrange the blocks in the circles and nail into the small blocks from both sides.

  10. Smooth with files where necessary
The dining room side was finished right after the wall was built. Metal lath was stapled down to the boards and then plastered and sanded smooth. Now the kitchen side is finally finished with tile as originally intended.