INSTRUCTIONS
1. Combine garlic, salt, sugar, lime zest, 2 teaspoons oil, cumin, pepper, and cayenne in bowl and mix to form paste. Reserve 2 teaspoons garlic paste for dressing.
2. Position chicken skin side up on cutting board and pat dry with paper towels. Leaving drumsticks and thighs attached, make 4 parallel diagonal slashes in chicken: 1 across drumsticks, 1 across leg joints; and 2 across thighs (each slash should reach bone). Flip chicken over and make 1 more diagonal slash across back of drumsticks. Rub remaining garlic paste all over chicken and into slashes. Refrigerate chicken for at least 1 hour or up to 24 hours.
3. 3A. FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour two thirds evenly over half of grill, then pour remaining coals over other half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
4. 3B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Turn primary burner to medium and turn other burner(s) to low. (Adjust primary burner as needed to maintain grill temperature of 400 to 425 degrees.)
5. Clean and oil cooking grate. Place chicken on cooler side of grill, skin side up. Cover and cook until underside of chicken is lightly browned, 9 to 12 minutes. Flip chicken, cover, and cook until leg joint registers 165 degrees, 7 to 10 minutes.
6. Transfer chicken to hotter side of grill, skin side down, and cook (covered if using gas) until skin is well browned, 3 to 5 minutes. Flip chicken and continue to cook until leg joint registers 175 degrees, about 3 minutes longer. Transfer to platter, tent loosely with aluminum foil, and let rest for 5 to 10 minutes.
7. Meanwhile, whisk remaining ¼ cup oil, lime juice, cilantro, oregano, and reserved garlic paste together in bowl. Spoon half of dressing over chicken and serve, passing remaining dressing separately.
