How To Cook: RIBEYE Steak! Recipe | Make the BEST, Perfect Grilled RIB EYE Steaks! Cook Perfect Steak on a Grill, Gas or Charcoal. Grill thick-cut Rib Steaks, also known as bone-in Ribeye steaks, Prime Rib, Cowboy Steaks, Scotch fillets or Rib Eye Steak.