Pat steaks dry. Generously season with salt and pepper; sprinkle with oregano and coriander. Let stand 5 minutes.
Heat a large cast-iron skillet over high. Swirl in 1 tablespoon oil. Add steaks in a single layer. Cook, undisturbed, until a brown crust forms on bottoms, about 4 minutes. Flip and cook, undisturbed, until a crust forms on other sides and a thermometer inserted into thickest parts reads 125 degrees for medium-rare, about 3 minutes more. Transfer to a plate.
Reduce heat to medium; wipe any blackened bits from bottom of skillet with a paper towel. Add remaining 2 tablespoons oil, bell peppers, onion, and basil sprigs; season with salt and pepper. Cook, stirring occasionally, until vegetables are golden and tender, 18 to 20 minutes. Add vinegar; cook until reduced by half, about 30 seconds. Add tomato sauce, accumulated juices from steak, and 1/3 cup water. Simmer, stirring a few times, until reduced and thickened slightly, about 2 minutes. Remove and discard basil.
Thinly slice steak against the grain. Serve over rice, with braised vegetables and basil leaves.