Sprinkle steaks with 1/4 tsp. each salt and pepper. Heat oil in a large frying pan over high heat. Add steaks and cook, turning once, until medium-rare, 10 to 12 minutes. Transfer to a cutting board; tent with foil.
Reduce heat to medium and add 1 tbsp. butter to pan. Add green garlic and garlic and stir until fragrant, about 1 minute.
Pour in broth, wine, and vinegar and cook, stirring to release browned bits, until reduced by two-thirds. Remove from heat and stir in remaining butter. Season with remaining 1/4 tsp. each salt and pepper and serve with sliced steak.
*Buy green garlic (harvested before the bulb is mature) at farmers' markets and Asian grocers in spring and early summer.