Quickly sear the beef fillets in a hot pan with olive oil for 30 to 60 seconds until browned all over and rare in the middle. Remove from the pan and leave to cool.

Finely chop the mushrooms with chestnuts and fry in a hot pan with olive oil, thyme leaves, and some seasoning. When the mushrooms begin to release their juices, cook over high heat for about 10 minutes until all the excess moisture has evaporated and you are left with a mushroom paste (known as a duxelles). Remove the duxelle from the pan and leave it to cool.

Cut the pastry in half, place it on a lightly floured surface, and roll each piece into a rectangle large enough to envelop one of the beef fillets. Chill in the refrigerator.

Lay a large sheet of cling film on a work surface and place 4 slices of Parma ham in the middle, overlapping them slightly, to create a square. Spread half the duxelle evenly over the ham.

Season the beef fillets, then place them on the mushroom-covered ham. Using the cling film, roll the Parma ham over the beef and tie the cling film to get a nice, evenly thick log. Repeat this step with the other beef fillet, then chill for at least 30 minutes.

Brush the pastry with the egg wash. Trim the pastry and brush all over with the egg wash. Cover with cling film and chill for at least 30 minutes. Remove the cling film from the beef, then wrap the pastry around each ham-wrapped fillet.

Meanwhile, make the red wine sauce. Heat the oil in a large pan, then fry the beef trimmings for a few minutes until browned on all sides. Stir in the shallots with the peppercorns, bay, and thyme and continue to cook for about 5 minutes, frequently stirring, until the shallots turn golden brown.

Pour in the vinegar and let it bubble for a few minutes until almost dry. Now add the wine and boil until nearly entirely reduced. Add the stock and bring it to a boil again. Lower the heat and simmer gently for 1 hour, removing any scum from the surface of the sauce until you have the desired consistency. Strain the liquid through a fine sieve lined with muslin. Check for seasoning and set aside.

When you are ready to cook the beef wellingtons, score the pastry lightly and brush it with the egg wash again, then bake it at Bake for approximately 35 minutes at 425°F until the pastry is golden brown cooked. Rest for 10 minutes before carving.

Meanwhile, reheat the sauce. Serve the beef wellingtons sliced, with the sauce as an accompaniment.