Pat the chicken breasts dry and lightly pound them to an even thickness, about 1/4 inch.
Dust each piece with a thin layer of flour on both sides. This helps the sauce cling and gives a touch of body.
Lay a slice of prosciutto on top of each chicken piece, tucking a sage leaf under the prosciutto or on top as you prefer.
Heat a large skillet over medium heat. Add the olive oil and a tablespoon of butter. When the butter sizzles, add the chicken, prosciutto side down.
Cook until the prosciutto edges turn lightly golden and the chicken is just cooked through, about 2 to 3 minutes per side depending on thickness.
Remove the chicken to a plate and keep warm. Deglaze the pan with white wine, scraping up any browned bits.
Reduce the heat and add the remaining butter. Let it melt, then swirl the pan to create a glossy sauce.
Add the chicken stock and let the sauce simmer for a minute or two to reduce slightly. Return the chicken to the pan to warm through and coat with the sauce.
Taste and season with a pinch of salt and pepper if needed. Serve the chicken with the pan sauce spooned over the top.