Soak the sweetbreads in cold water for several hours; drain. Bring them to a boil in one quart water with one teaspoon salt and the vinegar. Lower the heat and simmer for four minutes. Drain and place in cold water. When cool, remove connective tissues and tubes but not the top membrane. Press under a weight for several hours.
Preheat oven to moderate (350°F.).
Brown the onions and carrots lightly in half of the butter in a skillet. Turn them into a shallow baking dish. Arrange the sweetbreads over the vegetables.
In the same skillet, heat the shallots in the remaining butter and add the brown sauce. Add the wine and pour the mixture over the sweetbreads. Season with salt and pepper to taste.
Bake for about one hour, basting frequently with the liquid in the pan.