In a large heavy bottomed saucepot over medium-high heat, combine the Basic Tomato Sauce, ketchup, mustard, Worcestershire, sugar, ale, and hot sauce and bring to a simmer. Simmer until reduced by half and thickened, about 20 minutes.
Meanwhile, season the chicken pieces with salt and black pepper. Heat a large oven proof skillet over high heat and add the vegetable oil. Sear the chicken pieces on all sides until well-browned, about 3 minutes per side.
Add the prepared BBQ sauce making sure to cover all the chicken pieces. Add 1 cup of water if more liquid is needed to cover. Place the skillet into the oven and bake until the chicken easily falls off the bone and the sauce is slightly thickened and caramelized on top, about 25 to 30 minutes. Serve hot or serve cold as leftovers.
In a large heavy-bottomed pot or Dutch oven, heat the olive oil over medium heat.
Add the garlic and cook until fragrant but not browned, 1 to 2 minutes. Add the tomatoes, bring to a simmer, and cook until thickened slightly, about 15 minutes. Stir in sugar, and season with salt, to taste.
Let extra sauce cool completely and then seal in airtight containers. Refrigerate for up 1 week and freeze for up to 1 month.