Cut ribs into pieces, 2 to 3 ribs per section. Place in a large pot, layering with sliced onion and garlic cloves. Add salt and pepper, cover with water, and place over medium-high heat; bring to a boil, cover, lower heat, and simmer briskly until ribs are tender, 45 minutes to 1 hour. Remove rib pieces to a large rimmed baking sheet.

Mix together rub ingredients and, when ribs are cool enough to handle, coat on all sides with rub mixture. Cover tightly with plastic wrap or foil and refrigerate for at least 6 hours and up to overnight.

To finish, bring a grill to medium-high heat. Working in batches if necessary, grill ribs, turning occasionally, until hot through and nicely browned on both sides; baste with barbecue sauce, if desired, toward the end. Serve at once.