01 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
02 - Season beef medallions generously with salt and pepper. Heat olive oil in a skillet over high heat. Sear medallions for 1 minute per side until browned but still rare inside. Transfer to a plate and let cool completely.
03 - In the same skillet, melt butter over medium heat. Add shallots and garlic; sauté for 2 minutes until fragrant. Add mushrooms and thyme; cook until mushrooms release their moisture and it fully evaporates, about 8-10 minutes. Season with salt and pepper. Let cool completely.
04 - Roll out puff pastry on a lightly floured surface to about 1/8 inch thick. Cut into 8 squares large enough to wrap each medallion completely.
05 - Place a slice of prosciutto on each pastry square. Spread a spoonful of cooled mushroom duxelles over the prosciutto. Top with a seared beef medallion.
06 - Fold pastry over the beef to enclose completely, pinching seams firmly to seal. Place seam-side down on the prepared baking sheet.
07 - Brush pastry tops with beaten egg. Chill assembled wellingtons for 10 minutes in the refrigerator.
08 - Bake for 18-22 minutes until pastry is golden brown and crisp. Let rest for 5 minutes before serving to allow juices to redistribute.