On a plate, mix flour with 1 Tbsp. rosemary, 1 tsp. salt and 1/2 tsp. pepper. Dredge chicken cutlets in seasoned flour; shake to remove excess.
Warm 2 Tbsp. oil in a large skillet over medium-high heat. Add cutlets and cook until golden, 2 to 3 minutes per side. Remove to a plate; cover loosely. Wipe out skillet, leaving behind browned bits.
Place skillet over low heat and warm 1 Tbsp. oil. Add garlic and 1 Tbsp. rosemary; stir for 1 minute. Add chicken broth and lemon zest and juice, scraping up browned bits on the skillet. Raise heat to medium; boil until sauce has thickened, about 5 minutes. Season with salt and pepper. Return chicken with juices to skillet, turning to coat. Serve hot.