Step 1In an 8-inch skillet over low heat, melt the butter, then saute the diced shallot until soft, about 2 minutes. Add the mushrooms and cook 2 to 3 minutes until dry and nicely caramelized. Add the garlic and the parsley and cook for an additional minute. Spoon the mixture into a bowl and let cool.
Step 2Crumble the sausage into small pieces and stir it into the mushroom mixture. Season with one-fourth teaspoon salt, one-eighth teaspoon pepper and the thyme.
Step 3Place each piece of veal between 2 sheets of plastic wrap and, using a mallet or the bottom of a heavy pan, pound until very thin. Be careful not to break up the meat.
Step 4Season the veal with salt and pepper. Place a piece of veal vertically in front of you. On the side closest to you, place one heaping tablespoon of filling. Roll the end over the filling, then fold both long sides in as if to make a burrito, then roll it up to make a paupiette. To tie, place the rolled paupiette facing you vertically and center a piece of kitchen string around the back. Bring the ends toward you and tie a loose knot in front, then loop the string over itself again. Pull tight, then make a double knot. Rotate the paupiette so the knotted side is away from you and bring both strings toward you so they are taut. Tie in front in the same manner, then trim the ends. Cut three 10-inch pieces of string and tie them around the middle of the roll, spacing evenly and using the same knots. Trim the ends. Roll and tie the remaining paupiettes using the same technique.
Step 5Wipe the same skillet clean and heat the olive oil on medium high heat. Brown the paupiettes on all sides, about 8 minutes. Remove them to a plate, add the carrots to the pan and brown.
Step 6Remove the pan from the heat and add the white wine. Put the pan back on high heat and deglaze the pan by scraping up the brown bits on the bottom. Cook to reduce the wine slightly, then add the paupiettes, tomato sauce and bouquet garni. If the liquid does not totally cover the paupiettes, add a little water. Bring the liquid to a boil, reduce the heat to low and simmer covered for 30 minutes.
Step 7Remove the paupiettes to a shallow dish. Cook the cooking liquid until it is reduced to about one-half cup. Remove the string from the paupiettes. Pour the sauce over the paupiettes and refrigerate. Serve at room temperature.