Flatten chicken breasts to 1/4" thickness. Sprinkle with salt and pepper.  In a large nonstick skillet, heat 1 Tbsp each oil and butter. Cook chicken over high heat for 4 minutes per side or until juices run clear (or insert instant read meat thermometer in thickest part of chicken. Temperature should read 170 degrees F).

 

Remove chicken to serving platter. Add green onions, lemon juice, parsley, and mustard to skillet; cook and stir for 15 seconds. Add chicken broth and remaining oil and butter; stir until smooth. Pour sauce over chicken.