While your grill preheats, combine all dry spices in a small bowl: garlic powder, onion powder, smoked paprika, mustard powder, cayenne, salt, black pepper, light brown sugar, and dried oregano. Whisk together thoroughly to ensure even distribution, breaking up any clumps. This ensures every bite of chicken has consistent flavor rather than pockets of concentrated spice.
Pat the chicken drumsticks completely dry with paper towels—this is crucial for proper browning and crisping on the grill. Rub them all over with the olive oil, working it into all crevices and ensuring even coverage. I like to do this with my hands so I can feel where the oil has covered and where it hasn't.
Coat all sides of the oiled chicken drumsticks generously with the spice rub from Step 1, pressing it gently onto the surface so it adheres well. As you finish seasoning, preheat your grill to 400°F-450°F and let it reach temperature while your chicken sits for 2-3 minutes—this allows the seasoning to begin adhering and helps the chicken come to closer to room temperature for more even cooking.
Place drumsticks on the preheated grill in a single layer, spacing them at least an inch apart to allow heat circulation. Flip every 5 minutes, rotating them to ensure even exposure to the heat and to develop an evenly charred, golden exterior. Continue cooking for about 25 minutes total until the internal temperature reaches 185°F when measured at the thickest part of the thigh without touching bone—this ensures the meat is fully cooked and tender.
Transfer the cooked drumsticks to a clean plate and let them rest for 5 minutes before serving. This brief rest allows the juices to redistribute throughout the meat, keeping each drumstick moist and tender rather than releasing all the juices onto the plate the moment you bite into it.