In a large bowl combine beef, garlic powder, cumin, salt, and pepper; mix well. Shape into four 3/4-inch-thick patties.
For a charcoal grill, grill patties on the rack of an uncovered grill directly over medium coals for 14 to 18 minutes or until done (160°F), turning once halfway through grilling. Add a slice of ham and cheese to each burger the last 1 minute of grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place patties on grill rack over heat. Cover; grill as directed.).
Serve burgers on bread slices with pickles, onion and, if desired, tomato.