Heat 1 tablespoon butter in a frying pan. Add onions, salt and pepper. Sauté until onions are wilted. Add capers, garlic and rosemary; continue cooking over medium heat for 5 minutes. Set aside in the frying pan and keep warm.
Heat 1 tablespoon butter in a second frying pan large enough to hold the liver in a single layer. Blend flour with salt and pepper. Dredge liver in flour mixture and shake off excess. Sauté liver over high heat, about 2 minutes per side, until medium rare. Transfer to heated serving plate.
Replace the first frying pan with the onions back over high heat and add vinegar. Bring to a boil. Add 1 tablespoon butter and swirl around. Pour mixture over liver slices. Garnish with parsley.