Heat oven to 400ºF.
Line 9-1/2-inch tart pan with removeable bottom with crust; trim edge. Prick bottom with fork. Bake 10 to 12 min. or until lightly browned. Cool.
Meanwhile, heat oil in nonstick skillet on medium heat. Add onions; cook 10 min. or until caramelized, stirring occasionally. Spoon into crust; top with asparagus.
Beat next 4 ingredients with whisk until well blended. Add 1/4 cup Parmesan; mix well. Pour over asparagus; top with remaining Parmesan.
Bake 20 to 24 min. or until filling is slightly puffed and set in center.