Clean mushrooms with damp paper towels or a mushroom brush. Remove stems and chop.
Saute mushroom caps and stems in 2 tablespoons butter. Remove from heat; drain. Fill each cap with parsley. Set stems and caps aside.
Melt remaining butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add whipping cream and milk; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Add salt, pepper, and reserved mushroom stems.
Arrange cooked asparagus spears and mushroom caps on an ovenproof serving dish. Pour sauce over asparagus. Sprinkle with cheese. Place under broiler 3 minutes or until lightly browned.