Combine Ground Beef, onion, jalapeno, cilantro and 1/4 cup cheese in medium bowl, mixing lightly but thoroughly. Lightly shape into four 1/2-inch thick patties.
To grill (if preferred, a skillet version follows), place patties on grid over medium, ash-covered coals. Grill, covered, 8 to 10 minutes (over medium heat on preheated gas grill, 7 to 9 minutes), until instant-read thermometer inserted horizontally into center registers 160F, turning occasionally.
Place burgers in tortillas or buns; season with salt and black pepper, as desired. Top with desired toppings.
Alternative skillet version: Heat large nonstick skillet over medium heat until hot. Place patties in skillet; cook 10 to 12 minutes turning occasionally, until instant-read thermometer inserted horizontally into center registers 160F, turning occasionally. About 3 minutes before burgers are done, top evenly with remaining 1/4 cup cheese.