Build a lump charcoal fire and allow it to burn down to coals while you prepare your backstrap.
Begin by placing the towel in a dish and pouring on enough wine to completely soak it. Save remaining wine for the meal or drink it as you grill.
Start by soaking a clean cotton cloth with red wine.
Trim all fat, connective tissue and silverskin from the backstrap.
Squeeze excess wine from towel and spread the towel flat on your work surface. Sprinkle on a layer of salt most of the way across the towel and at least as wide as your backstrap section. Make the salt ¼- to ½-inch thick.
Place the backstrap along the long edge of the towel, directly on top of the salt. Season the surface of the backstrap with pepper and lay on several sprigs of fresh rosemary.
Place the backstrap on a layer of salt on the wine=soaked towel.
Roll the towel tightly around the backstrap, encasing the meat in a layer of salt. Tuck the ends of the towel into the roll, wrapping it like a burrito, so that the towel is wrapped tightly on all sides of the backstrap.
Use butcher’s twine to tie the towel tightly around the backstrap, then tie it from end to end so that the towel wrap is tight to the meat.
Wrap the backstrap tightly with the towel and tie with butcher’s twine.
Using tongs, place the wrapped backstrap directly into the coals. The wine in the towel will slow the burn process, but the towel will still char and smolder. Don’t worry about it and don’t move the backstrap for 8-10 minutes.
After the backstrap has cooked on one side, use the tongs to gently flip it so that the other side of the towel rests in the coals. Cook an additional 6-9 minutes. (Thicker backstraps or a more desired doneness than rare to medium rare should cook for the upper ends of the time span.)
Move the backstrap to a cutting board or sheet pan on or next to the serving area in view of your dinner guests. Allow the backstrap to rest for 5-10 minutes, then gently unwrap any remaining towel bits from the salt crust.
Use the back of your carving knife to gently break apart the salt crust, larger pieces are better and easier to remove from the cooked meat. Move the backstrap to a cutting board and use your knife to gently rake away any remaining salt, the rosemary, and any bits of charred cloth. Slice the backstrap into medallions for serving.