Preparation Heat 1 tablespoon butter with 2 tablespoons oil in a 12-inch heavy skillet over moderate heat until foam subsides, then cook onions with 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon rosemary, stirring occasionally, until softened and golden brown, about 30 to 35 minutes. Transfer onions to a plate and loosely cover with foil. Pat livers dry and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat remaining tablespoon oil in same skillet over moderately high heat until hot but not smoking, then cook livers, turning over once, until browned and just pink inside, 4 to 5 minutes. Transfer to plate with onions. Add grapes and remaining 1/4 teaspoon rosemary and sauté over moderately high heat, shaking skillet, 1 minute. Add vinegar and deglaze skillet, stirring and scraping up brown bits. Swirl in remaining tablespoon butter, remaining 1/4 teaspoon salt, and 1/4 teaspoon pepper. Pour over liver and onions and serve immediately.
Preparation Heat 1 tablespoon butter with 2 tablespoons oil in a 12-inch heavy skillet over moderate heat until foam subsides, then cook onions with 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon rosemary, stirring occasionally, until softened and golden brown, about 30 to 35 minutes. Transfer onions to a plate and loosely cover with foil. Pat livers dry and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat remaining tablespoon oil in same skillet over moderately high heat until hot but not smoking, then cook livers, turning over once, until browned and just pink inside, 4 to 5 minutes. Transfer to plate with onions. Add grapes and remaining 1/4 teaspoon rosemary and sauté over moderately high heat, shaking skillet, 1 minute. Add vinegar and deglaze skillet, stirring and scraping up brown bits. Swirl in remaining tablespoon butter, remaining 1/4 teaspoon salt, and 1/4 teaspoon pepper. Pour over liver and onions and serve immediately.