In a 6-qt. nonreactive pot, whisk together honey, 1⁄2 cup salt, Tabasco, 1 tbsp. pepper, and 8 cups hot water; let cool. Add pork loin and chill, covered, for up to 8 hours or overnight. Meanwhile, combine remaining salt and pepper with paprika, cayenne, sugar, garlic powder, onion, and chopped garlic in a bowl; set aside. Place apple juice in a bowl and draw it into a kitchen syringe; set aside.
Prepare your grill using the kettle grill, bullet smoker, or gas grill method, (see links for instructions) using apple wood chunks or chips (see Fuel and Flavor). Remove pork from brine and pat dry with paper towels; rub spice mixture all over pork and inject apple juice into pork in several places. Place loin on grill grate. Maintaining a temperature of 225°-250° (if using a kettle grill or bullet smoker, replenish fire with unlit coals, as needed, to maintain temperature; see instructions), cook until a thermometer inserted into the thickest portion reads 160°, 2–3 hours. Let pork rest for 15 minutes before slicing.