Heat grill to medium-high. Mix ground meat, cilantro, garlic, and coriander until just combined. Form into 4 patties (about 1/2 inch thick); sprinkle with salt. Grill burgers 8 to 10 minutes (for medium), turning once halfway through.
Stir together ketchup and curry powder. Serve burgers on buns with curry ketchup. Garnish with 2 tablespoon feta cheese, red onion, and cilantro, if desired.