Sprinkle the chicken cutlets on both sides with salt and pepper. Set aside 1 tsp. of flour. Spread the remaining flour out on a large plate and gently coat each chicken breast with flour. Set aside.
Stir in the butter, capers, mustard, lemon juice, and parsley. Serve each chicken breast with 2 tbsp of piccata sauce.
In a skillet or saute pan, melt half of the butter over medium high heat. Add half of the olive oil and a touch of cooking spray if needed. Add the chicken breast and cook for 4-5 minutes on each side until browned and just cooked through. Then set aside and tent with tinfoil to keep them warm. While the chicken is cooking, mix 1 tsp of flour into 3/4 cup of chicken stock and set aside.
Add the other 1/2 tbsp of olive oil, shallots, and garlic to the pan. Cook for two minutes until fragrant but not burnt. Add 1/2 cup of chicken stock and scrape all of the brown bits off the bottom of the pan. Cook for about 5 minutes until the chicken broth almost evaporates. Add the chicken broth you mixed with flour and stir until smooth. Let it reduce by half and then turn the burner to low.