Vegetable oil (for grill)
4 garlic cloves, finely grated
1 lemongrass stalk, top third trimmed, tough outer layers removed, finely grated
½ cup sugar
¼ cup unseasoned rice vinegar
2 tsp. crushed red pepper flakes
2 tsp. ground cumin
1 tsp. freshly ground black pepper
3 Tbsp. fish sauce
12 large chicken drumsticks (about 3 lb.)
Kosher salt
Prepare a grill for high indirect heat (for a gas grill, leave one or two burners off; for a charcoal grill, bank coals on one side); oil grate. Bring garlic, lemongrass, sugar, vinegar, red pepper flakes, cumin, black pepper, and ½ cup water to a boil in a small saucepan, stirring occasionally, and cook until reduced to ½ cup, about 8 minutes. Let cool and stir in fish sauce. Transfer half of sauce to a small bowl and set aside for serving.
Season chicken with salt. Place over indirect heat and cover grill with vent open (if you have one) and positioned over chicken. Grill, turning once or twice, until skin is browned and crisp and meat is nearly cooked through, 25–30 minutes. Uncover and move chicken to hotter part of grill. Continue to grill, turning often and basting with remaining sauce, until lacquered and lightly charred in places, 6–8 minutes longer. Serve with reserved sauce alongside.