Season the chicken with salt and black pepper and dust both sides lightly with flour.
Heat 1 tablespoon olive oil in a 12-inch skillet over medium-high heat and brown the mushrooms for 5 minutes, then transfer them to a plate.
Add the remaining oil and cook the chicken for 3 to 4 minutes per side, until it reaches 165°F, then move it beside the mushrooms.
Lower the heat, melt the butter and cook the garlic for 30 seconds before stirring in the broth.
Simmer for 2 minutes, return the chicken and mushrooms and turn them through the garlic-butter sauce.