Whisk broth, mustard, salt, pepper and 2 teaspoons flour in a small bowl until smooth.
Sprinkle both sides of the chicken with the remaining 1 tablespoon flour. Heat oil in a large nonstick skillet over medium-high heat. Cook the chicken in two batches, adjusting heat as necessary to prevent burning, until golden, about 2 minutes per side. Transfer the chicken to a plate; tent with foil to keep warm.