In a medium bowl, whisk together the peanut butter, water, lemon juice, soy sauce, dark brown sugar, garlic, ginger, red pepper flakes and salt until the mixture is well combined.
Put the drumsticks in a glass or ceramic bowl or resealable container, and cover with the peanut sauce, making sure the marinade thoroughly coats the chicken. Cover the bowl with a large plate, or seal the container, and let the chicken marinate in the refrigerator for at least 3 hours and up to overnight.
Position a rack in the middle of the oven and preheat to 375 degrees.
Line a 1 ½-quart baking dish (see headnote) with a piece of aluminum foil or parchment paper large enough to go up the sides, trimming off excess. Set aside. (You can bake the chicken directly in the pan, but this step makes clean-up considerably easier.)
Remove the chicken from the refrigerator and transfer it, along with the marinade, to the prepared baking dish. Season the chicken with the black pepper. Bake, uncovered, for 45 minutes, or until the internal temperature of the meat reaches 165 degrees.
Transfer the chicken to a serving plate, spooning the peanut sauce and cooked bits over the drumsticks. Sprinkle with the scallions, if desired.
Serve with white rice or egg noodles, either of which benefit from spoonfuls of the remaining peanut sauce.
