In a medium bowl, mix together milk and potato flakes. Stir in 1 tablespoon on onion soup mix.

Add ground beef and 1/4 teaspoon pepper. Mix together and form into 4 oval-shaped patties. Place on a plate and cover with plastic wrap. Refrigerate at least 30 minutes.

Melt 1 tablespoon butter in a large nonstick pan over medium-high heat. Add patties and cook until nicely browned on both sides, about 5 minutes per side. Transfer to a plate and set aside.

Add remaining 3 tablespoons butter and 1 tablespoon vegetable oil to pan and place over medium heat. Add sliced onion.

Once onion begins to soften, after about 2 minutes, add mushrooms and cook until mushrooms are browned and most of liquid has evaporated.

Sprinkle flour on top of onion/mushroom mixture. Stir and cook for 1 minute.

Stir in remaining onion soup mix and ketchup.

Gradually whisk in broth. Bring to a simmer.

Return patties to pan, cover, reduce heat to low, and cook 12 to 14 minutes.

Check for seasoning and add salt and pepper to taste.

Serve over mashed potatoes.