Cook the pappardelle in salted water according to the instructions on the package until al dente. Drain and keep the pasta warm. Carefully remove the thin white membrane, veins and any residual blood from the sweetbread. Wrap the sweetbread first in plastic wrap and then in aluminium foil. Twist the ends tightly. Simmer the sweetbread gently in water for 15 minutes. Remove the sweetbread from the water, let it cool and remove both wrappings.
Beat the eggs with the vinegar and the salt. Dredge the sweetbread in the flour, then in the beaten egg and finally in the breadcrumbs. Heat the oil to 170˚C (338°F). Deep-fry the sweetbread for 2 minutes until golden brown or fry it in a generous amount of oil in a frying pan. Remove the sweetbread from the oil and let it drain on paper towels. Clean the mushrooms. Cut the largest ones in half.
Heat the oil and butter in a frying pan and fry the mushrooms until they begin to brown. Pour in the white wine and let cook briefly. Stir in the crème fraîche and gently cook for 5 to 10 minutes until the sauce thickens. Add salt and pepper to taste. Peel, wash, dry and cut the carrots in long strips (julienne). Heat the butter in a frying pan and quickly fry the carrots. Deglaze with vinegar, add salt and pepper and keep warm.
Cut the sweetbread into slices. Distribute the slices over the plates. Make nests of pappardelle and place them next to the sweetbread. Pour the mushroom-wine sauce over the sweetbread and pasta.
Garnish with the julienne carrots.