Add 1 tablespoon of vegetable oil to a skillet, set on medium-low heat, and saute onion (1/2 cup) and garlic (3 cloves) until translucent, about 7 minutes. Let cool.
In a mixing bowl, stir together cooled sautéd onions and garlic, milk (1/3 cup), egg (1), Worcestershire sauce (1 tablespoon), dijon (1 tablespoon), salt (3/4 teaspoon), pepper (1 teaspoon), and bread crumbs (1/2 cup) to form a paste. Mix in ground sirloin (1 pound) and shape into 4 equal-sized oval patties.
In a medium skillet, cook 2 patties at a time for 4-5 minutes per side or until browned; Repeat with remaining patties. Drain grease from the skillet and discard. Remove to a platter and keep warm.
Melt butter (2 tablespoons) in the skillet. Add onion slices on top of brown bits. Reduce the heat to medium-low and cook onions, about 5 minutes, until soft and translucent. Add mushrooms (8 ounces) and 1/2 teaspoon salt and continue to cook until liquid has evaporated, about 5-7 minutes.
Stir in tomato paste (1 tablespoon). Sprinkle mixture with flour (2 tablespoons). Cook flour for 1-2 minutes, stirring often, to toast and remove the flour taste. Remove from heat.
Slowly stir in beef broth (1 1/2 cups), water with dissolved Better Than Bouillon, and sherry (2 tablespoons) until combined and bring to a simmer
Nestled the meat patties into the sauce. Cover. Reduce heat and simmer gently for 15 minutes, or until the patties are cooked through. Remove from heat, sprinkle with parsley (1-2 tablespoons), and serve warm.