Bring a pot of water to a boil and blanch the sweetbreads for about five minutes. Drain and plunge into a bowl of ice water. Peel the membrane from the outside of the sweetbreads. It might be necessary to pull apart the lobes to get the little shreds of membrane out, but don't break the sweetbreads up too much. Drain the excess water.
Combine the flour, salt, and pepper. Dust the sweetbreads with the mixture.
Heat the butter in a skillet over medium heat until it bubbles. Sauté the sweetbreads until browned lightly on all sides. Don't be concerned that they might not be cooked throughout; there's yet another stage of cooking coming. Keep the sweetbreads warm.
Pour off the excess butter, but don't wipe the pan. Lower the heat to medium-low, and add the Calvados. Bring to a boil, whisking the bottom of the pan to dissolve the juices and butter. Be careful; Calvados is highly alcoholic, and the fumes may flame. (That's okay, but be ready to deal with it.)
When the Calvados is almost all gone, add the apple juice, mustard, and mushrooms. Sauté the mushrooms until soft. Add the cream and bring to a boil, stirring the pan to blend the ingredients. Be careful not to let the cream foam over.
Taste the sauce and add salt and pepper as needed. Return the sweetbreads to the pan and cook until heated through. Serve with orzo pasta.