Preheat smoker to 275° Fahrenheit.
Add 1 tablespoon brown sugar, 2 teaspoons garlic powder, 2 teaspoons salt, 2 teaspoons smoked paprika, 1 teaspoon onion powder, 1 teaspoon freshly cracked black pepper, and ½ teaspoon chili powder to small bowl. Stir until spices are well-blended. Set bowl aside.
Place 12 medium bone-in, skin-on chicken drumsticks on cutting board. Pat each drumstick completely dry on all sides with paper towels.
Use basting brush (or clean paper towel) to brush olive oil on all sides of each drumstick, covering each drumstick completely. Return drumsticks to cutting board.
Sprinkle spice mixture over drumsticks, coating all sides of each drumstick fully. Gently massage spice mixture into skin of drumsticks with hands, being careful not to tear skins. Mix together additional spice rub as needed depending on size of chicken legs.
When all drumsticks have been seasoned fully, transfer drumsticks to preheated smoker. Place chicken legs directly onto smoker grate and close lid.
Smoke chicken legs 1 hour 15 minutes, then begin checking internal temperature of chicken legs. Continue smoking drumsticks until internal temperature reaches 165° Fahrenheit according to internal meat thermometer.
When chicken reaches desired internal temperature, preheat broiler to low. Position oven rack so that baking sheet sits approximately 10 inches beneath broiler.
Carefully transfer chicken legs to large baking sheet, making sure to place chicken legs in one even layer without stacking or overlapping. Note: for even crispier skins, fit baking sheet with wire rack first, then place drumsticks on wire rack.
Place baking sheet beneath preheated broiler. Broil drumsticks 4 to 5 minutes or until skins have crisped, then carefully remove baking sheet from oven and set aside.
Allow chicken to rest until internal temperature reaches 170° Fahrenheit, no more than 10 minutes. Serve chicken legs warm with desired sides.