a plastic squeeze bottle; a large domed lid or metal bowl; four 6-inch wooden skewers
For the BBQ sauce: Heat the oil over medium-high heat in a heavy-bottomed medium saucepan. Add the onions and cook until soft, 3 to 4 minutes. Add the garlic and cook for 1 minute. Add the ketchup and 1/2 cup water, bring to a boil and simmer for 5 minutes. Add the ancho chile powder, brown sugar, mustard, paprika, vinegar, Worcestershire, honey, molasses, chile de arbol and chipotle chile and simmer, stirring occasionally, until thickened, an additional 10 minutes.
Transfer the mixture to a food processor and puree until smooth. Season with salt and pepper. Pour into a medium bowl and allow to cool to room temperature. Put about 1/3 cup of the BBQ sauce in a small bowl; reserve the remaining BBQ sauce in the medium bowl for spooning on top and serving.
For the coleslaw: Whisk together the mayonnaise, vinegar, granulated sugar, celery salt, onion and some salt and pepper in a large bowl. Add the cabbage and carrot and stir to combine; season with more salt and pepper if needed. Let sit at least 15 minutes before serving.
For the burger: Heat a grill, grill pan or cast-iron griddle to high heat. Brush the grill grates, pan or griddle with the oil.
Whisk together the ancho, paprika, mustard powder, coriander, cumin, oregano, chile de arbol, 1 teaspoon salt and 1/2 teaspoon pepper in a small bowl.
Form the meat into four 6-ounce burgers. Brush the burgers with oil, season with some of the rub and sprinkle with salt and pepper on both sides. Grill until the burgers are golden brown and slightly charred on the bottoms, 3 to 4 minutes. Brush with the BBQ sauce from the small bowl (discard any unused sauce). Flip the burgers and continue to cook to medium doneness, about 4 minutes longer. Spoon a little of the reserved BBQ sauce on each burger and top each with a slice of cheese. If using a grill pan or griddle, fill a squeeze bottle with water and squirt the pan. Cover the burgers with a grill lid, large domed lid or large metal bowl and count to 10 -- until the cheese is melted
Place the burgers on the bun bottoms and spoon some more of the BBQ sauce on top. Top with some of the coleslaw and a few pickles. Top with a few potato chips, if desired. Put the bun tops on and stick a 6-inch wooden skewer through each.
The BBQ sauce will keep for 1 week in the refrigerator stored in a tightly sealed container.