Place the oven rack in the middle of the oven and preheat to 450˚F. Oil a rimmed baking sheet.

Place the tortilla chips, 2 teaspoons of the chili powder, the cumin, and 1/4 teaspoon of salt in the bowl of a food processor. Pulse until coarsely ground, then transfer to a shallow dish.

Whisk the egg in a small bowl with the remaining 2 teaspoons of chili powder.

Sprinkle the drumsticks with 1/2 teaspoon of salt. Dip each drumstick in the egg mixture and let the excess drip off. Coat with the tortilla crumbs, gently pressing them to make them stick to the chicken. Arrange on the prepared baking sheet. 

Bake, undisturbed, until cooked through, 40-45 minutes. Let rest at room temperature for 5 minutes before serving.