1. Slaw: In a medium bowl, toss ingredients to blend.
2. Burgers: Prepare an outdoor grill or heat a stovetop grill pan to medium.
3. In a medium bowl, gently mix beef, 1/4 cup of the barbecue sauce (or barbecue sauce mixture), chili powder, cumin, and salt. Divide mixture evenly and shape into 4 patties, each about 3/4-inch thick.
4. Brush hamburger buns with oil, then toast on grill, 1 to 2 minutes; set aside.
5. Grill burgers 3 to 4 minutes per side for medium-rare, brushing with the remaining 1/4 cup sauce.
6. Place a piece of lettuce on bottom of each bun; top with burger, then slaw. Replace top half of bun.
