Pulse garlic with 2 tbsp chili powder, balsamic vinegar, 2 tbsp brown sugar, cayenne and salt in a food processor until it forms a paste. Rub over ribs. Refrigerate at least 2 hours or overnight.

Place ribs in a very large pot. Add beer. Ribs will not be totally submerged. Boil, then reduce heat to medium-low. Simmer, covered, turning ribs occasionally, until fork-tender, 45 min to 1 hour. Transfer ribs to a platter. Discard liquid.

Stir cider vinegar with 1 cup brown sugar, coffee, remaining 2 tbsp chili powder and chili-garlic sauce in a medium saucepan. Boil, then reduce heat to medium-high. Boil, uncovered, until reduced by almost half, about 6 min.

Preheat barbecue to medium-low. Brush ribs with sauce. Oil grill, then barbecue ribs, turning and basting often, until glazed and hot, 10 to 12 min.