Pat turkey dry and season with salt and pepper. Dredge half of turkey slices in flour, shaking off excess. Heat 1 1/2 tablespoons oil in a 12-inch heavy skillet over high heat until hot but not smoking, then cook turkey until browned on both sides and just cooked through, about 4 minutes total. Transfer to a platter and keep warm, covered. Dredge and cook remaining turkey with another 1 1/2 tablespoons oil in same manner.
Add remaining tablespoon oil to skillet and cook garlic over moderate heat, stirring, until fragrant, about 30 seconds. Add broth and deglaze over moderately high heat, scraping up brown bits. Boil until broth is reduced to about 3/4 cup. Stir in lemon juice, capers, parsley, and salt and pepper, to taste. Add butter and swirl with a whisk until a smooth sauce is formed. Return turkey to skillet with any juices on platter and simmer until heated through, about 1 minute. Garnish with sage and rosemary leaves.