Debone veal chops. When deboned, each veal chop should be approximately 5 ounces each). Trim silver skin away and wrap each around rib eye muscle. Secure with toothpick or string. Refrigerate, covered. Photo of veal rib chops by Le Quois of Quebec.
In a large frying pan, melt 1 1/2 tablespoons butter. Add Chanterelle mushrooms and sautover high heat. Add salt, pepper, garlic, and parsley. Cover to release water from mushrooms and then uncover to let moisture evaporate. Remove from heat and transfer mixture to a large bowl; set aside. Wipe frying pan clean.
In the cleaned frying pan, add 1 tablespoon butter; saute onion and carrot over medium heat. Add shrimp. Increase heat to high and sautapproximately 1 to 2 minutes. Reduce heat to low and add brandy or cognac; cook approximately 4 to 6 minutes or until shrimp are pink and opaque in center (cut to test). Remove from heat and add to the mushroom mixture.
In a heavy frying pan (I use my cast-iron frying pan) over medium-high heat, heat remaining butter. Salt and pepper each side of veal chops. Sear the steaks, moving them with tongs a little so they do not stick to the bottom, for approximately 4 minutes per side. Cook until medium-rare and an internal thermometer registers 125 degree F. (use a meat thermometer to test for doneness). Remove from the pan, cover loosely with aluminum foil and let rest 5 to 10 minutes before serving. During this time the meat continues to cook (meat temperature will rise 5 to 10 degrees after it is removed from the oven) and the juices redistribute.
Deglaze pan with veal or meat stock until reduced by half. Add any juice from settle from the cooked veal chops. Add cream and cook on medium-high heat a few minutes until mixture begins to thicken. Stir in vegetables and shrimp mixture.
To serve, place veal chops on individual serving plates. Top with vegetable/shrimp mixture. Sprinkle with tarragon and serve.
* If you are nice to your butcher, he or she will do this for you.