Cut the Pieces
See cut list. To lay out the curved sides, first mark the back edge of a blank at each shelf location: 5, 18, and 29 inches from the bottom. Add ¾ inch to the depth of each shelf, then measure and mark that distance from the back edge at each shelf location. Tack a brad at each mark, and tack one near the top and bottom edges, inset ¾ inch from the back. Next, bow a thin batten between each pair of brads and use it to trace four shallow arcs. Gang the two side blanks and cut along the lines with a jigsaw.
Drill the Dowel Holes
For the horizontal dowels, drill ½-inch-deep holes every 2 inches in the front and back rails. For the diagonals, offset the holes in the beveled faces of the top and front rails ¼inch from the first set.
Assemble the Rack
Glue the short dowels into the back rail, then glue the front rail onto their free ends. Glue the diagonal dowels into the beveled faces of the front and top rails.
Build the Cabinet
Shim the back panel ¼ inch above your benchtop. Mark the shelf and rail locations on the side pieces and stand them up against the back panel. Place the shelves and rails at their marks, and screw into them through the sides and the back. Install the cup pegs and the French cleat. Paint the piece and hang it.