On a work surface, place 2 cutlets at a time between 2 sheets of parchment paper. With a smooth mallet or rolling pin, pound until thin. Cut each cutlet into ½-inch (1 cm) wide strips.
In a very hot, large, non-stick skillet over high heat, quickly brown one-third of the meat at a time in the butter. Season with salt and pepper. Set aside on a plate.
In the same skillet over high heat, brown the onion and mushrooms. Season with salt and pepper. Add the flour. Continue cooking for 1 minute, stirring constantly. Deglaze with the wine and let reduce by half. Add the cream and veal and let simmer until the sauce thickens. Adjust the seasoning.