How to Make It
In a large skillet, melt 1 tablespoon of the butter. Add the sage leaves and cook over moderate heat, turning once, until crisp, about 4 minutes. Transfer the sage leaves to paper towels to drain.
On a work surface, arrange the veal scaloppine in pairs that are roughly the same size and shape; season very lightly with salt and pepper. Working with 1 pair of scaloppine at a time: Set half a slice of prosciutto in the center of 1 scaloppine, leaving a narrow border all around. Top with one-sixth of the pecorino and another half slice of prosciutto and the second piece of veal scaloppine. Using a meat pounder, gently pound the scaloppini to a uniform thickness, pounding around the edges to seal. Repeat with the remaining veal, prosciutto and pecorino.
In each of 2 large skillets, melt 1 tablespoon of the butter in 2 tablespoons of the olive oil. Dust the stuffed scaloppine with flour, tapping off the excess. Add 3 to each skillet and cook over high heat, turning once, until browned, about 4 minutes. Transfer the scaloppine to a large platter.
Divide the shallots between the skillets and cook over moderate heat, stirring, until softened, about 2 minutes. Off the heat, add 1/4 cup of the Cognac to each skillet, scraping up any browned bits stuck to the bottom. Simmer over moderate heat until nearly evaporated, about 1 minute. Add half of the cream and chicken stock to each skillet and bring to a boil. Season with salt and pepper and boil until the sauce is reduced to 1/2 cup, about 2 minutes. Strain the sauce into a heatproof cup and wipe out the skillets.
Return the sauce to the skillets and whisk 1 tablespoon of butter into each. Return the scaloppine to the skillets along with any accumulated juices and simmer over moderate heat, turning once, until coated with sauce, about 1 minute. Transfer the scaloppine to plates and spoon the sauce on top. Garnish with the fried sage leaves and serve right away.