Preheat oven to 400°F (200°C).
Pat the 8 chicken drumsticks dry with paper towels. If any skin or excess fat remains, remove it. Place the drumsticks in a large bowl and season with kosher salt to taste.
In a small bowl, combine 3 tbsp Dijon mustard, 1 tbsp light mayonnaise, 1 crushed clove garlic, the zest and the juice of 1 lime, and 3/4 tsp black pepper. Mix until smooth.
Pour the mustard-lime mixture over the chicken in the large bowl. Toss the drumsticks until they are evenly coated.
Lightly spray a large baking pan with nonstick cooking spray. Arrange the coated drumsticks in a single layer in the pan.
Sprinkle 1 teaspoon dried parsley evenly over the top of the chicken.
Bake in the preheated oven until the chicken is cooked through, about 35 minutes (internal temperature should reach 165°F/74°C).
If you want a golden-brown finish, move the pan under the broiler for 2 to 3 minutes—watch closely to avoid burning.
Remove the chicken from the oven and let rest a few minutes before serving.