Cut up chicken, leaving drumsticks and thighs attached. Season chicken with salt and freshly ground black pepper. Refrigerate, covered, until ready to use (up to 24 hours).
For sauce: In large nonreactive saucepan, melt butter. Add onion, garlic, and salt. Cook over low heat until onion is tender. Add crushed red pepper, paprika, chili powder, and black pepper; cook and stir for 1 minute.
Add water, vinegar, brown sugar, and Worcestershire sauce; bring to a simmer. Stir in molasses. Whisk in tomato paste until smooth. Bring to a simmer over low heat. Cook, uncovered, for 10 to 15 minutes or until sauce is thickened, stirring occasionally. Taste for seasoning, adding additional salt if needed. Remove 1-1/2 cups of the sauce to prepare chicken. Store remaining in the refrigerator; reheat to serve.
For chicken: Preheat oven to 325 degrees F. Heat 1/4 inch oil in a 12-inch skillet over medium heat. Working in batches, place chicken, skin side down, in skillet. Cook until well browned, turning once, about 5 minutes.
Transfer browned chicken to two 2- to 3-quart rectangular glass or nonreactive baking dishes. Place skin side up, adding breast portions to one dish and leg portions to the other. Add 2 tablespoons water to each baking dish.
Spoon reserved 1-1/2 cups barbecue sauce over chicken.* Cover chicken with parchment paper and then cover tightly with foil. (Refrigerate until ready to bake). Bake leg portions for 70 to 75 minutes and breast portions for 30 to 40 minutes (170 degrees F).
Increase oven temperature to 450 degrees F. Uncover chicken and spoon on additional sauce. Bake, uncovered, for 10 to 15 minutes or until well-glazed and meat is very tender. Serve with remaining barbecue sauce. Store any remaining barbecue sauce, covered, in the refrigerator for up to 1 week.
*Be sure that the sauce used on the uncooked chicken is kept separate from sauce for serving.