Place the first 9 ingredients in a large bowl and whisk to combine. Add the drumsticks and toss to coat.
Preheat the oven to 375 degrees F.
Line a baking sheet with parchment paper. Spread the panko on a wide plate. Coat one of the drumsticks with the panko, gently pressing it on to help it adhere. Set the drumstick on the baking sheet. Repeat with the remaining drumsticks.
Bake for 40 minutes, or until the chicken is cooked through.
Note: Panko, coarsely textured Japanese-style breadcrumbs, can be found in the Asian aisle. If unavailable, regular breadcrumbs can be substituted.
Recipe Options: For spicy tasting chicken drumsticks, replace 1/8 cup of the mayonnaise with Dijon mustard. For a sweet taste, drizzle the drumsticks with a tablespoon or two of honey 10 minutes before they are done. Use this method to coat chicken thighs, instead of drumsticks. Baking time may be five minutes longer, depending on the size of the thighs.