In a 12-inch skillet over medium-high, heat 1 teaspoon oil until barely smoking. Add the onion and cook, flipping the rings once, until well browned on both sides, about 6 minutes. Transfer to a plate and wipe out the skillet.
Season the steaks with salt and pepper. In the same skillet over medium-high, heat 1 tablespoon of the remaining oil until shimmering.
Add the steaks, reduce to medium and cook, flipping once, until well browned on both sides and the centers reach 120°F (for medium-rare), 10 to 15 minutes. Transfer to a platter and let rest for 10 minutes.
Meanwhile, pour off and discard the fat in the skillet, then add the remaining 1 tablespoon oil, the garlic, bay and seared onion.
Cook over medium, stirring, until the garlic begins to brown, about 2 minutes. Stir in the soy, both citrus juices, 3 tablespoons water and any accumulated meat juices, then bring to a simmer.
Off heat, add the butter and stir until melted. Remove and discard the bay, then taste and season with salt and pepper. Thinly slice the steaks and return to the platter, then spoon the sauce over.
