Heat 1 tablespoon butter and the oil in a large saute pan over medium-high heat. Add veal chops, and sear until golden, 5 to 6 minutes per side. Transfer to a plate, and keep warm.
Add the onion and garlic to the pan, and saute until softened, about 5 minutes. Add the mushrooms, and cook, tossing occasionally, until they have released all of their juices and most of the liquid has evaporated. Add the wine, and cook, scraping up any browned bits from the bottom of pan with a wooden spoon, until the liquid has evaporated, about 2 minutes. Stir in the stock and cream, return chops to pan, and bring to a boil. Reduce heat, cover, and simmer gently 30 minutes. Continue cooking, uncovered, until meat is very tender and sauce has thickened, 20 to 25 minutes. Season with salt and pepper.
Meanwhile, place potatoes in a large saucepan of cold, salted water, and bring to a boil. Reduce heat, and simmer gently until tender, about 15 minutes. Drain; pass potatoes through a potato ricer, and return to saucepan. Stir in the remaining 2 tablespoons butter and the milk, and season with salt and pepper. Cover, and set aside until ready to serve.
Pour warm sauce over the chops and mashed potatoes, and serve with greens on the side.