Shape beef into 6 oval patties. Melt butter in large skillet and add oil. Heat until foaming. Add green onions and sauté until softened; stir in garlic and sauté for 30 seconds. Add beef patties and cook to desired degree of doneness. Season with salt and pepper. Set beef patties aside to keep warm on a hot platter.
In same skillet, sauté mushrooms until limp and add to the warm beef patties.
To prepare Mustard Cream Sauce, deglaze pan with dry white wine. Reduce volume by half. Add Dijon mustard, heavy cream, tomato and capers. Heat slowly until hot but do not boil. Pour Mustard Cream Sauce over beef and mushrooms. Sprinkle parsley over top to garnish, if desired.