Line a 13x9x2-inch baking pan with foil; coat with nonstick cooking spray. Rinse mushrooms; pat dry. Remove stems, hollowing out centers of mushroom caps. Chop stems, reserving 2/3 cup (discard remaining stems). Arrange mushroom caps, stem sides up, in prepared pan.
Heat olive or vegetable oil in a medium skillet. Cook chopped mushroom stems, onion, and garlic in hot oil for 3 minutes. Stir in shrimp and parsley; heat through. Remove from heat; stir in bread crumbs, wine or sherry, basil, and pepper. Spoon shrimp mixture into each mushroom cap. Cover pan with foil.
Bake in a 350 degree F. oven for 10 minutes; remove foil. Bake 10 minutes more or until mushrooms are heated through. Immediately remove with slotted spoon or spatula. Serve hot. Makes 24 appetizers.