Combine ground beef and 1/4 cup salsa in large bowl, mixing lightly but thoroughly.
Divide beef mixture into 4 equal portions and lightly flatten into thin patties. Place one stuffed pepper in center of each patty. Wrap the beef around the pepper to enclose, sealing seams and forming a ball. Flatten balls into patties about 4-5 inches across and 1 inch thick.
Place patties on grill over medium ash-covered coals. Grill covered, 15-16 minutes to 165°F internal temperature, turning occasionally.
Spread 1 Tbsp. chile con queso evenly over top of each burger. Sprinkle with tomato and olives and serve on hamburger buns with additional salsa as desired.
