For the sautéed mushroom mixture
Season the meat with salt and brown all over the surface in a pan with olive oil. Remove the meat and deglaze the pan with the wines to collect the cooking juices. Place the meat and wines in an oven dish with high sides with the liquid level a quarter of the way up the meat. Cook in a preheated oven at 180ºC for 35-40 minutes. If you do not have enough liquid, you can add a little water or stock.
Place the cooking liquid with the sugar in a saucepan and cook over a medium heat until it has the consistency of syrup. For the sautéed mixture, soak the dried mushrooms in hot water for 15 minutes, drain and chop. Cut the fresh mushrooms into quarters and sauté them in a pot with very hot oil until golden brown. Remove and set aside. In the same pot, cook the onion with oil over a medium heat and stir until caramelised*. Add the soaked and fresh mushrooms and garlic, and cook for 5 more minutes. Season with salt and thyme, and blend the sautéed mixture.
Cut the meat when cold into thin slices. In a rectangular container with non-stick paper in the base, make alternate layers of meat and sautéed mushroom mixture. Sandwich two layers of cheese slices between the layers of meat and mushrooms. Finish the mille-feuille with a last layer of the sautéed mushroom mixture. Gently press the mille-feuille down and place in the freezer for one hour before cutting. Cut portions and heat them in the oven at 180ºC. Serve with the cooking juices.
This is an ideal dish for parties because it can be prepared in advance and even frozen in portions.
To ensure that the mushrooms become golden brown and retain their juices, make sure that the sauté pan is very hot, avoid adding too many at a time and allow them to cook for at least one minute before stirring.