Position an oven rack in the middle of the oven and preheat the oven to 400 degrees F. Line a baking sheet with aluminum foil.
Rub the drumsticks with the garlic, season with salt and arrange far from one another on the prepared baking sheet. Bake on the middle rack until the chicken is cooked through (165 degrees F) and the juices run clear, 25 to 30 minutes.
In a medium bowl, mix the cookies with 1/2 cup warm water; crush the cookies with the back of a spoon until they form a paste. Whisk in the peanut butter and soy sauce with an additional 1/4 cup warm water if needed. Stir in the lime juice, red wine vinegar, hot sauce, garlic powder, red pepper flakes and ginger. Taste for seasoning.
Toss the chicken in the sauce and serve immediately.