Using a meat mallet, pound the veal cutlets, one at a time, between 2 sheets of plastic wrap until each piece is about 1⁄8 inch thick. Lightly season with salt (little is needed, as prosciutto is salty) and pepper to taste.
Lay 2–3 slices of prosciutto atop each piece of veal, gently pressing prosciutto against veal to adhere. Place 2–3 sage leaves on top of the prosciutto and stitch them into the veal with toothpicks. Place the flour on a large plate. Dredge each piece of veal in the flour, shake off any excess, and set aside.
In a 12-inch skillet, heat 2 tablespoons of the oil and 2 tablespoons of the butter over medium-high. Add 2 pieces of veal and cook, turning once, until the prosciutto side is crisp and the veal side is lightly browned, about 1 minute per side. Transfer the meat to a paper towel-lined plate; drain and discard the oil and butter from the skillet. Repeat this process with more oil, butter, and the remaining meat. Remove and discard the toothpicks.
Drain and discard the oil and butter from the skillet; place over high heat. Add the marsala; cook, scraping up browned bits, until reduced by half, 1–2 minutes. Add the stock; reduce by half, about 3 minutes. Stir in the remaining 4 tablespoons of butter; reduce heat to medium. Return meat to skillet; cook, turning occasionally, until sauce thickens slightly, 1–2 minutes. Transfer to a platter and serve. (Alternatively, drizzle the pan sauce over the meat and serve.)