Cook vegetables in boiling water for about 8 minutes so that the lima beans get just tender. Let cool. Whip cream to stiff peaks. Fold mayonnaise into whipped cream. Add vegetables, pepper, and cheese, reserving some cheese for topping.
Pour into a 13 x 9-inch casserole dish (2 1/2 or 3 quarts). Top with remaining grated cheese. Heat about 30 minutes at 350 degrees.