Place flour, salt, and pepper in plastic bag and shake with chicken until breasts are thoroughly coated. Melt butter, making sure not to burn. Stir in olive oil. When oil and butter are bubbling, add chicken breasts, shaking off extra flour when removing from bag. Cook chicken on medium-high until crispy and golden brown.
While chicken is cooking, combine cream, garlic, and mustard in small bowl. Transfer the chicken to a warm platter. Reduce heat to medium and add cream to pan juices, stirring constantly until sauce is bubbling and slightly thickened. Pour sauce over chicken, garnish with parsley, and serve.
