Preheat grill to 350° to 400° (medium-high) heat. Sprinkle steaks with 1 1/2 tsp. salt and 1 tsp. pepper. Grill steaks, covered with grill lid, 9 to 12 minutes on each side or to desired degree of doneness.
Remove from grill, and rub 3 Tbsp. Citrus-Chile Butter onto steaks. Cover steaks with aluminum foil; let stand 5 minutes.
Meanwhile, toss onions with olive oil; season with remaining 1/2 tsp. salt and 1/4 tsp. pepper. Grill onions, without grill lid, 2 minutes; turn and grill 1 more minute.
Uncover steaks, and cut diagonally across the grain into thin slices. Serve with grilled onions and remaining Citrus-Chile Butter.
*Beef strip steaks (about 2 inches thick) may be substituted.