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 4 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.
Preheat to the oven to 400 degrees F. Line a baking sheet with parchment paper or a silicone baking mat.
On a work surface, roll 1 sheet of puff pastry to a 10 by 14-inch rectangle. Put teaspoon-sized mounds of mushroom mixture on the pastry, evenly spacing them in 4 rows of 3. 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. Working 1 at a time, pull 2 opposite sides of pastry up over each beef piece, then fold the ends over the top to make a packet. Invert and arrange the packets seam side down on the baking sheet and press them lightly to seal the pastry. Repeat with the remaining beef, mushrooms, and pastry.
Bake the Wellingtons until golden brown, 20 to 25 minutes. Remove from the oven to a serving platter and let cool at least 10 minutes before serving.