After ribs have come to room temperature (about 30 minutes), remove membrane, which is attached to the underside of the rack of ribs. Discard brine and season very liberally with your favorite rib rub, if using. Wrap ribs in heavy duty aluminum foil.
If you're using charcoal, light your coals and pile them all onto one side of the grill, leaving the other side empty. The empty side is the side you'll cook over indirect heat, at 350-400 degrees F. Cook for 90 minutes (45-minutes per side).
After you cook your ribs over indirect heat for 90-minutes, you'll remove your St. Louis-Style Ribs from the foil packet and grill over direct heat (directly over hot coals or flames) for one hour (30 minutes on each side).
Start testing for doneness at the one-hour mark – once the meat begins to pull away from the bones. This is easy to do with a fork. You also can twist a rib bone a little bit; you should feel it give easily but not fall apart from the meat. Allow ribs to rest for 10 minutes, before cutting and serving.