Preheat a cast-iron skillet or griddle to medium-high or high.
Melt 3 tablespoons butter in a large skillet over medium-high heat. When it foams, add mushrooms and brown. Season with salt and pepper, add shallots and thyme, and stir 2-3 minutes more. Stir in 1/4 cup beef stock and HP sauce; reduce heat to low.