Form the burgers into patties and make the fillings the night before serving. Put the two together right before you're ready to grill.
Divide meat into 8 equal parts. Flatten 4 portions into 4-inch patties. Place one-fourth (about 2 tablespoons) of one of the fillings in the center of each patty, spreading to within 1/2 inch of the edges.
Flatten the remaining 4 meat portions into 4-inch patties and gently place each on top of the filled patty, pressing the edges together to seal. Sprinkle garlic salt and pepper on each burger. For a charcoal grill, grill burgers on the rack of an uncovered grill directly over medium coals for 14 to 18 minutes or until an instant read thermometer inserted near the center registers 160 degree F, turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place burgers on grill rack over heat. Cover and grill as above.) Remove burgers from grill. Makes 4 burgers.
In a small bowl, mix tomato, jalapeno pepper, cilantro, and green onion.
In a small bowl, combine tomato, feta cheese, red onion, olives, red wine vinegar, olive oil, and dried oregano. Cover and chill in refrigerator for at least 30 minutes before using.
In a small bowl, combine mayonnaise, Parmesan, green onion, and olives.