Process the onion with the water in a food processor until pureed and the mixture resembles slush, about 30 seconds. Strain the mixture through a fine-mesh strainer into a liquid measuring cup, pressing on the solids with a rubber spatula or wooden spoon to obtain ½ cup juice. Some solids may seep through, that's okay. Discard remaining solids that remain in strainer.
In a medium bowl, whisk together the onion pulp, ketchup, molasses, vinegar, Worcestershire, mustard, liquid smoke, hot pepper sauce, and black pepper.
Heat the oil in a large nonreactive saucepan over medium heat until shimmering but not smoking. Add the garlic, chili powder, and cayenne and cook until fragrant, about 30 seconds. Whisk in the ketchup mixture and bring to a boil; reduce the heat to medium-low and simmer gently, uncovered, until the flavors come together and the sauce is thickened, about 20 minutes. Cool the sauce to room temperature before using. The sauce may be refrigerated in an airtight container for up to one week or frozen for up to three months.
Cook's note: The recipe as written makes what I would call a "thick and spicy" taste with the spicy being just right but not too hot. If you want more of a sweet sauce, substitute 1 teaspoon hot pepper sauce with 1 tablespoon brown sugar. For a very spicy sauce, double the hot pepper sauce and add the full ¼ teaspoon cayenne pepper.