In a pan, gently cook the sliced onion, carrot, celery with dried thyme, sage, bay leaf, allspice berries, peppercorns, and olive oil until vegetables are tender. Allow to cool completely.

Season beef filets with salt. Place in a ziplock bag with the cooled marinade, then add dry white vermouth and cognac. Refrigerate for 2-3 hours.

Remove filets from marinade (reserve the marinade for sauce). Pat filets dry and sear quickly in hot oil until browned on all sides. Return to refrigerator while preparing other components.

Process mushrooms until finely minced. Squeeze out juices and reserve for the sauce.

Sauté the mushrooms with minced shallots in butter for 7-8 minutes until dry and separated. Add 1/2 cup Madeira wine and cook until liquid evaporates. Stir in the pâté and set aside.

Roll out puff pastry sheets. For each Wellington, lay down a slice of prosciutto, spread some mushroom mixture, place a seared filet on top, then add more mushroom mixture. Wrap the pastry around the filet like a package, sealing edges with egg wash.

Brush the tops with egg wash and chill for at least 30 minutes.

Preheat oven to 375°F (190°C). Bake Wellingtons for about 25 minutes until golden brown. If pastry browns too quickly, tent with foil. Use a meat thermometer to check for desired doneness.

While Wellingtons bake, prepare the sauce. Combine reserved marinade, mushroom juices, beef broth, and tomato paste. Simmer for about an hour until reduced to 2 cups.

Remove any fat from the surface of the sauce. Mix cornstarch with 1/4 cup Madeira wine and stir into the sauce to thicken. The sauce should be rich and velvety.

Let Wellingtons rest for 5-10 minutes before serving. Slice carefully and serve with the Madeira sauce.