Heat 2 tablespoons of the butter and the oil in a large, heavy skillet over high heat. When the butter foams, add the scaloppini, making sure not to crowd the skillet. If you need to, cook the veal in two batches. Season with salt. Cook until the veal is lightly golden on both sides, about 2 minutes. Transfer the veal to a plate.

Add the wine, balsamic vinegar, and the remaining butter to the skillet. Cook over high heat and stir quickly to dissolve the meat deposits attached to the bottom of the skillet. When the wine is reduced by half, 3 to 4 minutes, return the veal to the skillet. Reduce the heat to medium and mix briefly until the veal is well coated with the sauce, 30 to 40 seconds. Serve at once with bit of sauce over each serving.