Melt 1 T butter in skillet with 1 T olive oil. Add onion and cook over low heat, stirring occasionally until golden, 15-20 minutes. Remove to bowl. Add shallots to pan and quickly sauté. Set aside. Turn heat up to medium high, add mushrooms and more butter and oil if necessary. Quickly cook mushrooms until they are cooked through and golden, stirring often. Set aside.

Lay puff pastry out on parchment lined baking sheet. Pinch edges up forming rim. Spread sauce over dough. Top with onions, mushrooms, asparagus and shallots. Sprinkle with cheese. Bake at 400 for 25 minutes or until pastry is golden and cooked through. Cut into 4 large squares for serving or smaller squares for appetizers.