Position a rack in the center of the oven and heat the broiler to high. Put the drumsticks in a medium bowl. Drizzle them with the olive oil and toss to coat. Sprinkle in the cumin, chili powder, sugar, 1/2 tsp. salt, and a few grinds of pepper; toss again to coat evenly. Arrange the drumsticks on a wire rack set over a foil-lined rimmed baking sheet. Broil the chicken in the center of the oven, turning once after 10 minutes, until fully cooked and browned in spots, about 20 minutes total.
While the chicken cooks, gently mix the tomatoes, avocado, onion, cilantro, lime juice, and 1 tsp. salt in a mixing or serving bowl. Serve alongside the chicken.
Serve with black beans and rice or tortilla chips.
nutrition information (per serving):
based on four servings;
Photo: Scott Phillips