Heat a gas or charcoal grill to high. Brush the grill grates with oil.
For the coleslaw: Combine the carrot, cabbage, onion, vinegar, mayonnaise, oil and sugar in a large bowl. Season with salt and pepper to taste. Let the slaw sit at least 15 minutes before serving.
For the spice rub: Whisk together the ancho chile powder, paprika, coriander, cumin, mustard powder, oregano, cayenne and 1 teaspoon each salt and pepper in a small bowl.
For the burgers: Divide the meat into 4 equal portions (about 6 ounces each). Shape each portion with your hands into a round patty, about 3/4 inches thick. Use your thumb to make a divot in the center of each burger. Sprinkle both sides of each burger with salt and pepper. Sprinkle the spice rub on one side of the burgers then brush with oil. Grill, spice rub-side down first, covered, until golden brown and slightly charred, about 4 minutes per side for medium.
While the burgers cook, toast the buns on the grill until lightly charred, 10 to 15 seconds. Set aside.
Add 2 slices of cheese to the tops of each burger. Cover the burgers with the grill lid, large domed lid or large metal bowl and count to 10 until the cheese is melted.
Place the burgers on the bottom buns and spoon about 2 tablespoons of the BBQ sauce on each. Top with the sliced pickled jalapenos, some of the coleslaw and the top buns and serve immediately.