Smash the garlic cloves, sprinkle with a generous pinch of salt, and, with the flat side of a large knife, mash and smear mixture to a coarse paste.

Stir garlic paste, the 1/4 teaspoon salt, cola, ketchup, vinegar, Worcestershire, chili powder, 1 teaspoon black pepper, 1/2 teaspoon hot sauce, and allspice together in a small saucepan. Bring to a boil, reduce heat, and simmer until thickened, about 45 minutes. Allow to cool slightly, stir in the lime juice, and season with black pepper and hot sauce, to taste.

Know-How: Barbecue sauces are all about balance: a sweet note offset by sour with a jolt of spice, all of which flourish in a cloud of smoke. There are lots of ways to work this magic-thick, thin, and in-between. Concocting a signature sauce is compulsory in some barbecue circles. Start with this basic riff and play with variations to suit your style.