In a skillet cook 6 cloves garlic, minced, in 2 tablespoons olive oil over medium heat until just starting to brown. Remove from heat. Carefully add 1/3 cup orange juice, 1/3 cup lemon juice, 1 teaspoon ground cumin, and 1/2 teaspoon each salt and ground black pepper. Bring to boiling; reduce heat. Simmer, uncovered, about 5 minutes or until slightly reduced. Remove from heat; cool. Whisk before serving.
lace burgers on broiler pan and broil 3 to 4 inches from heat for 12 to 14 minutes or until meat is done (160 degreeF), turning once halfway through broiling. Add a slice of ham and cheese to the top of each patty. Broil about 30 seconds more or until cheese begins to melt. (Broil buns or rolls for 45 to 60 seconds to toast.)
To toast buns, place them on the grill rack for 1 to 2 minutes while your burgers finish grilling.