Place the 21 x 60 x ¾-inch plywood on a worktable. Remove the drawer(s) from the vanity cabinet and turn it upside down. Set the cabinet on one end of the plywood aligning it with the 21-inch edge. Secure it to the plywood with the 1¼-inch drywall screws.
Measure from the other end of the plywood and make a mark at 2 inches. Put the framing square on the mark and draw a line across the 21-inch width of the plywood.
Apply glue to one edge of the piece of 2 x 2 x 18-inch lumber. Place it on the side of the line that is away from the edge from which it was drawn. Secure the 2 x 2 to the plywood with 1¾-inch drywall screws. Clean up excess glue immediately with a damp cloth.
Next, stand the piece of 21 x 30 x ¾-inch plywood against the 2 x 2 x 21-inch lumber. Secure it through the 2 x 2 lumber with 1¾-inch drywall screws. Turn the desk over so the front of the desk is facing down.
Run a bead of glue on the ¾-inch edges of the desk. Place the 58¾ x 28 x ¼-inch plywood on the desk; align it with the top of the desk and the cabinet. Secure it to the end with the cabinet on it first with the 4-penny box nails and then the rest of the desk.
Turn the desk over so the front is facing up. Apply glue to the front edge of the top and secure the piece of 1 x 2 x 60-inch lumber to it with 6-penny finish nails.
Measure and cut the veneer edge band 1 inch longer than each of the remaining sides of the top. Install the veneer pieces one at a time with a hot iron. Sand them after installation.