Combine port (or cherry juice) and dried cherries in a small saucepan. Bring to a boil, reduce heat to low and simmer gently for 5 minutes. Cover and remove from heat.
Meanwhile, whisk broth and cornstarch in a small bowl until smooth. Season cutlets on both sides with salt and pepper. Place flour on a large plate and dredge the cutlets, shaking off excess flour.
Heat 2 teaspoons oil in a large nonstick skillet over medium heat. Add half the cutlets and cook until golden brown and just cooked through, 2 to 3 minutes per side. Transfer to a platter, cover and keep warm. Add the remaining 2 teaspoons oil to the pan and repeat with the remaining cutlets. Transfer to the platter and cover.
Heat butter in the pan over medium heat. Add onion and rosemary and cook, stirring often, until the onion is tender, 3 to 4 minutes. Whisk the cornstarch mixture and stir into the pan along with the cherry mixture and vinegar. Reduce heat to low, return the turkey and any accumulated juices to the pan and cook, turning to coat with sauce, until heated through, 1 to 2 minutes. Serve the turkey topped with the cherry sauce.