Gently gut gills from mushroom caps with a spoon and cut off stems; rinse each cap thoroughly under cold water and pat tops dry with paper towel. Coarsely chop stems and set aside. Brush 2 teaspoons of the oil over mushroom caps; place oiled sides down on a 15"x10" jelly roll pan or baking sheet.
Heat remaining 1 tablespoon oil in a non-stick skillet over medium-high heat. Add asparagus, shallots, garlic and chopped mushroom stems. Cook 5 to 6 minutes or until vegetables are crisp-tender, stirring occasionally.
Remove from heat; stir in tomato, salt and pepper. Spoon mixture into mushroom caps. Combine bread crumbs and cheese; sprinkle evenly over mushrooms. Sprinkle parsley flakes and a bit of olive oil over bread crumbs. Bake 10 to 12 minutes or until hot and crumbs are golden brown.