Heat the olive oil in a large skillet over medium-high heat. Pat the beef dry with a paper towel and season all sides with salt and pepper. Quickly sear the beef on 2 sides only until deep golden brown, about 2 minutes total; do not overcook. Transfer to a plate to cool.
Add the mushrooms and cook until beginning to brown and release liquid, about 5 minutes. Add the shallots and continue cooking until mushroom mixture dries out, is golden brown and shallots are soft, about 10 minutes. Remove from heat and cool.
On a work surface, roll 1 sheet of puff pastry. Put 1/4 teaspoon mounds of mushroom mixture on the pastry, evenly spacing them in 5 rows of 4. Top the mushroom mound with a piece of beef, seared side up. With a sharp knife, cut the pastry into even squares around the meat and mushrooms. Beat one egg and using a small paint brush and working 1 at a time, brush beateb egg on edges of pastery around the beef and mushroom. pull 2 opposite sides of pastry up over each beef piece, then fold the ends over the top to make a packet. Repeat with the remaining beef, mushrooms, and pastry.
Preheat to the oven to 400 degrees F. Line a baking sheet with parchment paper.
Bake the Wellingtons until golden brown, about 10-15 minutes. Remove from the oven to a serving platter and let cool at least 10 minutes before serving.