Combine flour and 1 teaspoon pepper. Pat chicken dry with paper towels. Dredge chicken in flour, shake off any excess. Arrange on a tray and lay six sage leaves over each one. Place 1 slice of prosciutto on top of each chicken breast, pressing lightly to adhere.
Heat 2 to 3 tablespoons oil in a skillet over medium heat. Add cutlets to pan, prosciutto-side down (careful not to overcrowd); cook until golden brown and prosciutto is crisp, 2 to 3 minutes. Turn cutlets over and cook until light golden brown (add more oil if needed), about 2 minutes more.
Transfer to an oven-safe platter or rimmed baking sheet and keep warm in oven. Repeat with remaining oil and cutlets.
In the same skillet, stir in white wine to deglaze the pan and simmer over med-low heat until reduced to about 1/3 cup (tip the pan to gauge the amount at the bottom edge of the pan) 5 minutes. Stir in lemon juice, stock, and garlic; simmer 3-5 minutes to reduce. Turn heat to low and whisk in butter, 1 tablespoon at a time.
Turn off heat and stir in parsley; taste, and season with salt and pepper. Return chicken and any collected juices to the skillet with the sauce allowing the chicken to rest in the sauce for a few minutes to keep warm.
Serve cutlets with sauce drizzled over the top.
Notes
It is important to flatten the chicken breasts so the meat cooks evenly.