Place the chicken breast halves between sheets of waxed paper or plastic wrap. Pound slightly with mallet until they are of even thickness. Sprinkle with salt and pepper.
In a large skillet, heat 1 tablespoon each of butter and oil.
Cook the chicken over high heat for 3 minutes on each side, or until cooked through. Do not cook overcook the chicken or it will be dry. Transfer the chicken to a warm serving platter and cover with foil.
Add the onions, lime juice, parsley, brandy (if using), and mustard to the skillet. Cook 15 seconds, whisking constantly.
Whisk in the broth. Stir until the sauce is smooth. Whisk in the remaining tablespoon of butter.
Pour the sauce over the chicken. Serve immediately.