Chef John's Chicken Marsala

Season chicken breasts all over with salt and pepper.

Melt 1 1/2 tablespoons butter and olive oil in a skillet over medium heat. Cook chicken breasts, skin-side down, in hot butter and oil until browned, about 5 minutes. Flip and cook until breasts are almost cooked through, about 5 minutes more. Transfer chicken breasts to a plate.

Melt 1 1/2 tablespoons butter in the same skillet over medium-high heat. Saute mushrooms with a pinch of salt and a pinch of pepper in hot butter until mushrooms are golden, 5 to 7 minutes. Add minced shallot; cook and stir until softened, 2 to 3 minutes. Sprinkle flour over the top and cook and stir until the bitterness of the flour cooks off, 3 to 4 minutes.