Preheat oven to 475 °F. Coat a wire rack with cooking spray and set it on a large rimmed baking sheet.
Mix breadcrumbs, paprika, onion powder and salt in a shallow dish. Drizzle with oil and mash with a fork until the oil is thoroughly incorporated. Lightly beat egg with a fork in another shallow dish. Dip the drumsticks into the egg, then press into the breading mixture until evenly coated on both sides. (Discard any remaining mixture and/or egg.) Place the chicken on the prepared rack.
Bake the chicken until golden and an instant-read thermometer inserted into the thickest part of a drumstick without touching bone registers 165 °F, 25 to 30 minutes.
To prepare sauce: Combine yogurt, mustard, honey and pepper in a small bowl. Serve the sauce with the drumsticks.
Make Ahead Tip: Cover and refrigerate the sauce (Step 4) for up to 3 days.
Note: To make your own breadcrumbs, trim crusts from whole-wheat bread. Tear bread into pieces and process in a food processor until very fine. Spread on a baking sheet and bake at 250°F until dry, about 10 to 15 minutes. One slice of bread makes about 1/3 cup dry breadcrumbs.
Cut Down on Dishes: A rimmed baking sheet is great for everything from roasting to catching accidental drips and spills. For effortless cleanup and to keep your baking sheets in tip-top shape, line them with a layer of foil before each use.