In a cast iron skillet (or saucepan), mix together all the sauce ingredients, until combined. Bring to a boil over medium heat, then reduce to medium-low and simmer until thickened, about 8-10 minutes. Stir in 3 TBS butter. Cool completely and set aside a 1/2 cup for use during grilling. Reserve the rest for serving.
Lightly brush steaks with olive oil. Salt and pepper both sides of the steaks and let set out at room temperature for 15-30 minutes.
Turn grill on to SCREAMING HOT grill the steaks with the lid closed, until cooked to your desired doneness, 6-7 minutes for medium rare,(if you cook it past medium rare you may as well grill a tennis shoe)turning once and brushing the tops and sides liberally with the sauce. Remove from grill and let rest for 3-5 minutes. Serve steaks warm with the reserved sauce on side.