Place each chicken breast half between two pieces of plastic wrap. Using the flat side of a meat mallet, lightly pound chicken to 1/4-inch thickness. Discard plastic wrap. In a shallow dish, combine flour, salt, and pepper. Coat chicken pieces with flour mixture.
In a 12-inch skillet, melt butter over medium heat. Add chicken to skillet. Cook about 4 minutes on each side, or until no pink remains in the chicken. Transfer chicken to a platter, reserving drippings in skillet. Cover to keep warm.
In the same skillet, add the olive oil. Add garlic and sauté until fragrant, about 30 seconds. Pour in white wine and bring to simmer, then add cream, mustard and lemon juice. Simmer until the sauce thickens slightly, about 1-2 minutes. Season with salt and pepper.
Serve chicken over cooked white rice, if desired. Spoon extra sauce on top of each serving and garnish with parsley.