01 - Pat the beef medallions dry with paper towels. Season all sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a skillet over high heat. Sear beef medallions for 30 seconds per side until well-browned on the exterior but still rare inside. Transfer to a plate and let cool completely.
03 - In the same skillet, melt butter over medium heat. Add shallot and garlic; sauté for 1 minute until fragrant. Add finely chopped mushrooms and thyme; cook, stirring frequently, until all liquid evaporates and mixture becomes a concentrated paste-like consistency, about 8 minutes. Season with salt, pepper, and parsley. Cool completely.
04 - On a lightly floured surface, roll out puff pastry to 1/8-inch thickness. Cut into 8 equal squares, approximately 4 inches each.
05 - Lay a piece of prosciutto on each pastry square. Spread a spoonful of cooled mushroom duxelles over the prosciutto. Place a seared beef medallion in the center.
06 - Fold pastry corners over the beef, creating a neat parcel. Brush edges with beaten egg and press firmly to seal. Place seam-side down on a parchment-lined baking sheet.
07 - Brush tops with egg wash. Refrigerate assembled Wellingtons for 10 minutes to firm the pastry. Meanwhile, preheat oven to 400°F.
08 - Bake for 18 to 22 minutes, or until pastry is deep golden brown and puffed. Let rest for 5 minutes before serving to allow juices to redistribute.