1. Pat steak dry and put on a plate. Stir together 1 teaspoon cumin and 1/2 teaspoon salt, and sprinkle on steak to coat. Let steak sit at room temperature for 15 minutes.
2. Finely chop enough of mango to measure 1/2 cup. Whisk together juice, cilantro, shallot, oregano, garlic, oil, and remaining 1 teaspoon cumin and 1/2 teaspoon salt. Stir in mango. Reserve salsa.
3. Preheat grill. Grill steaks on a lightly oiled rack, uncovered, over moderately high heat, turning once, for 8 to 10 minutes total for medium rare. Let stand 10 minutes.
4. Serve steaks topped with salsa. Makes 4 servings.