Cuban-Style Grill-Roasted Pork

1. FOR THE PORK AND BRINE: Cut 1-inch-deep slits (about 1 inch long) all over roast, spaced about 2 inches apart. Dissolve sugar and salt in 6 quarts cold water in large container. Stir in garlic and orange juice. Submerge pork in brine, cover, and refrigerate for 18 to 24 hours. Remove pork from brine and pat dry with paper towels.
2. FOR THE PASTE: Pulse garlic, cumin, oregano, salt, and pepper in food processor to coarse paste, about 10 pulses. With processor running, add orange juice, vinegar, and oil and process until smooth, about 20 seconds. Rub paste all over pork and into slits. Wrap meat in plastic wrap and let sit at room temperature for 1 hour.
   3A. FOR A CHARCOAL GRILL: Open bottom vent halfway. Light large chimney starter three-quarters filled with charcoal briquettes (4-1⁄2 quarts). When top coals are partially covered with ash, pour into steeply banked pile against side of grill. Set cooking grate in place, cover, and open lid vent halfway. Heat grill until hot, about 5 minutes.
   3B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Turn primary burner to medium-high and turn off other burner(s). (Adjust primary burner as needed during cooking to maintain grill temperature of 300 to 325 degrees.)
3. Clean and oil cooking grate. Place roast skin side up on cool side of grill. Cover (position lid vent over meat if using charcoal) and cook for 2 hours. During final 20 minutes of cooking, adjust oven rack to lower-middle position and heat oven to 325 degrees.
4. Transfer pork to wire rack set in rimmed baking sheet and cook in oven until skin is browned and crisp and meat registers 190 degrees, 3 to 4 hours.
5. Transfer roast to carving board and let rest for 1 hour. Remove skin in 1 large piece. Scrape off and discard top layer of fat, then cut meat away from bone in 3 or 4 large pieces. Cut pieces of meat against grain into 1⁄4-inch-thick slices. Scrape excess fat from underside of skin and cut into strips. Serve.

CUBAN-STYLE OVEN-ROASTED PORK
Adjust oven rack to lower-middle position and heat oven to 325 degrees. Place paste-rubbed pork, skin side down, on wire rack set in rimmed baking sheet and cook for 3 hours. Flip roast skin side up and continue to cook until meat registers 190 degrees, about 3 hours longer, lightly tenting roast with aluminum foil if skin begins to get too dark.