Pound the veal medallions lightly between two sheets of heavy plastic (such as in a food storage bag). Blend the flour, salt, and pepper, and sprinkle veal scallops very lightly with salt, pepper and flour.
Heat 2 Tbs. of the butter in a heavy skillet until it bubbles. Cook veal, two or three pieces at a time, for about a minute on each side. Remove to a platter and keep it warm in the oven. Add more butter to the skillet to finish the rest of the veal.
When all the veal is cooked, add the onions to the skillet and cook until transparent. Add the Marsala and bring to a boil, whisking the pan to dissolve the browned bits from the veal.
Add the mushrooms. Lower the heat and allow to simmer until the mushrooms are tender and the sauce has thickened.
Stir in the demi-glace if you have it. Return to a simmer, then add the parsley. Adjust seasonings with salt and pepper.
Return the veal to the skillet (along with all juices that may have collected on the platter). Stir lightly to coat with the sauce. Serve on warm plates, perhaps with polenta.