In a large bowl, whisk the eggs together with the salsa and seasonings. Stir in the bread crumbs. Add the meat and mix together until it is all blended. Mix in the cheese.
Shape the meat mixture into 4 burgers, each about 4 inches wide and 3/4 inch thick.
Place the burgers on a greased grill about 4 inches above hot coals. Cook 6-8 minutes per side. Or heat vegetable oil in a large frying pan set over medium low heat. Add the burgers and sauté uncovered, about 8 minutes per side.