Snap off the tough ends of the asparagus and discard. Wash the asparagus thoroughly.
Put the tips of the asparagus together evenly and, with a sharp knife, cut off any parts extending beyond about 6 inches.
Cut these trimmings into 1-inch pieces. Place them in a covered casserole with the water.
Cook in the microwave oven for 2 to 3 minutes, depending upon their toughness. Add the remaining asparagus, putting the butt end toward the outer edges of the baking dish. Cover and cook until barely tender. (This should take about 6 to 8 minutes.).
Remove asparagus to a serving dish, putting the cut pieces in the bottom of the dish and placing the spears attractively on top.
Melt the butter in a small container in the microwave oven. Pour evenly over the asparagus. Sprinkle on the parmesan cheese, salt and pepper. Return to the microwave oven to reheat for 30 seconds. Serve.