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 degrees 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. Drizzle with some of the Mojo Sauce sauce; pass remaining sauce.
In a medium skillet cook minced garlic in olive oil over medium heat until just starting to brown. Remove from heat. Carefully add orange juice, lemon juice, ground cumin, salt, and black pepper. Bring to boiling; reduce heat. Simmer, uncovered, about 5 minutes or until slightly reduced. Remove from heat; cool. Whisk before serving.