Place the chicken between two sheets of plastic wrap and pound to an even 1/4-inch thickness — this is the 30-minute enabler: thin cutlets sear in 3–4 minutes and cook through without ever touching the oven. Pat dry and season with 1/2 teaspoon salt and 1/4 teaspoon pepper.

Lay 2 sage leaves on each cutlet and drape 2 slices of prosciutto over the top, pressing gently so they adhere. Dredge very lightly in flour, shaking off the excess. Secure with toothpicks if the prosciutto lifts (remove before serving).

Heat the olive oil in a large skillet over medium-high heat until shimmering. Lay the cutlets prosciutto-side down and sear undisturbed for 3 minutes, until the prosciutto is crisp and golden. Flip and sear 2–3 minutes more, until the chicken reads 165°F on an instant-read thermometer. Transfer to a plate and tent loosely with foil.

Reduce the heat to medium. Add 1 tablespoon of the butter and the garlic; cook 30 seconds until fragrant. Pour in the white wine, scraping up all the browned bits, and let it bubble for 1 minute. Add the broth and lemon juice.

Simmer until the sauce reduces by about a third and looks slightly syrupy, about 3–4 minutes. Off the heat, swirl in the remaining 1 tablespoon butter for a glossy finish. Season with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper.

Return the cutlets to the skillet and spoon the sauce over them; let them warm for 1 minute. Shower with parsley and serve with lemon wedges and plenty of sauce for spooning.