1. Adjust oven rack to middle position and heat oven to 200 degrees. Combine flour and 1 teaspoon pepper in shallow dish.
2. Pat cutlets dry with paper towels. Dredge chicken in flour, shaking off any excess. Lay cutlets flat and sprinkle evenly with minced sage. Place 1 prosciutto slice on top of each cutlet, pressing lightly to adhere; set aside.
3. Heat 2 tablespoons oil in large skillet over medium-high heat until beginning to shimmer. Add sage leaves and cook until leaves begin to change color and are fragrant, about 15 to 20 seconds. Using slotted spoon, remove sage to paper towel-lined plate and reserve for garnish. Add garlic cloves to oil and cook for just a couple of minutes just to infuse the oil, then remove. Add half of cutlets to pan, prosciutto-side down, and cook until light golden brown, 2 to 3 minutes. Flip and cook on other side until light golden brown, about 2 minutes more. Transfer to wire rack set on rimmed baking sheet and keep warm in oven. Repeat with remaining 2 tablespoons oil and cutlets, then transfer to oven to keep warm while preparing sauce.
4.Stir in wine, scraping up any browned bits, and simmer until reduced to about 1/3 cup. Stir in lemon juice. Turn heat to low and whisk in butter, 1 tablespoon at a time. Off heat, stir in parsley and season to taste with salt and pepper. Remove chicken from oven and place on platter. Spoon sauce over cutlets before serving. Garnish with fried sage leaves and lemon wedges.