01 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
02 - Season beef medallions 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.
03 - In the same skillet, melt butter over medium heat. Add shallots and garlic, sauté for 2 minutes. Add mushrooms and thyme; cook until mushrooms release moisture and it evaporates, about 8-10 minutes. Season with salt and pepper. Let cool completely.
04 - Roll out puff pastry on a floured surface to about 1/8 inch thick. Cut into 8 squares large enough to wrap each medallion.
05 - Place a slice of prosciutto on each pastry square. Spread a spoonful of mushroom duxelles over the prosciutto. Top with a beef medallion.
06 - Fold pastry over the beef to enclose, pinching seams to seal. Place seam-side down on the prepared baking sheet.
07 - Brush pastry with beaten egg. Chill assembled wellingtons for 10 minutes in the fridge.
08 - Bake for 18-22 minutes, or until pastry is golden brown and crisp. Let rest for 5 minutes before serving.