Measure and cut the plywood to slightly overhang the top of the cart, leaving a gap of at least 2 inches at the cart handle, to allow you to grip the handle.
Sand all surfaces of the plywood, including the sides, and stain to your desired shade, then allow to dry.
Measure the widest circumference of the Egg, at its center, and draw a circle about 2 inches smaller on your plywood where you wish the Egg to rest.
Drill a small hole on one edge of the outline on the plywood as a starting point, and cut with a jigsaw to create a hole. Sand the edges of the hole until smooth.
Brush polyurethane clear finish on the top surface of the plywood board according to manufacturer's instructions, then allow to dry.
Measure the tops of the four support posts on the utility cart. Drill holes 1/2 inch deep into small squares of 1-inch scrap hardwood. Place the wood pieces over the support posts and glue the undrilled upper surface.
Place the plywood board over the wood scrap pieces and clamp at all four corners. Allow glue to dry, then remove the clamps.
Lower the Egg into its new resting place.