Clean mushrooms with damp paper towels. Remove stems, reserving stems for another use.
Saute mushroom caps in 1 tablespoon hot olive oil in a large skillet over medium-high heat 5 minutes. Remove from skillet, and drain on paper towels. Add green onions to skillet; saute over medium-high heat until tender. Remove from heat; stir in 1/3 cup Parmesan cheese and next 4 ingredients. Set aside.
Crumble goat cheese evenly into mushroom caps. Spoon breadcrumb mixture evenly into mushroom caps over goat cheese, and sprinkle evenly with remaining Parmesan cheese. Arrange mushrooms on rack of a broiler pan coated with cooking spray. Broil 5 1/2 inches from heat (with electric oven door partially opened) 2 to 3 minutes or until lightly browned.