In a bowl, season ground beef with 1 teaspoon salt and 1/2 teaspoon pepper. Form into 6–8 even patties; handle them gently.

Heat butter or oil in a large skillet over medium heat. Add onions and cook until translucent, about 4–5 minutes. Add garlic and cook for an additional 30 seconds.

Nestle the raw patties into the skillet among the onions. If using mushrooms, add them now.

In a measuring cup, whisk together the beef broth, Worcestershire sauce, and tomato paste or mustard until combined. Sprinkle flour over the onions and patties so it can absorb fat and start to cook.

Pour the broth mixture evenly over the patties. Bring to a gentle simmer, then reduce heat to low and cover.

Simmer covered for about 18–25 minutes, until patties reach an internal temperature of 160°F (71°C) when checked with an instant-read thermometer.

Uncover, increase heat to medium, and simmer for 2–4 minutes to reduce and thicken the gravy. If it's still thin, stir in a cornstarch slurry (1 tsp cornstarch + 2 tsp water) and simmer until glossy.

Taste and adjust salt and pepper if necessary.

Let patties sit in the covered skillet off the heat for 3–5 minutes before serving to redistribute juices.