Using a meat mallet, pound the veal cutlets, one at a time, between 2 sheets of plastic wrap until each piece is about 0.5cm thick. Lightly season with salt (little is needed, as prosciutto is salty) and pepper, to taste.
Lay 1 slice of prosciutto on top of each piece of veal, gently pressing prosciutto against veal to adhere. Place 1 sage leaf on top of the prosciutto and stitch them into the veal with a toothpick.
Place flour on a large plate. Dredge each piece of veal in flour, shake off any excess, and set aside.
Heat 2 tbsp of the oil and 2 tbsp of the butter in a skillet over medium-high heat.
Add half of the meat and cook, turning once, until 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. Repeat with more olive oil, butter, and remaining meat. Remove and discard the toothpicks and keep the meat slices warm.
Drain and discard half of the oil and butter from the skillet; then place back over high heat. Add white wine; cook, scraping up browned bits, until reduced by half, 1–2 minutes.
Add chicken stock; reduce by half, about 3 minutes. Stir in remaining 4 tbsp. of butter; reduce heat to medium, until sauce thickens slightly, 1–2 minutes.