Heat olive oil in a skillet over medium-high heat. Sear the beef fillets on all sides until browned. Remove and let cool.
In the same skillet, add mushrooms and cook until all moisture is evaporated. Let cool.
Brush the beef fillets with Dijon mustard.
Roll out puff pastry and cut into squares large enough to wrap each fillet. Place a spoonful of mushrooms in the center of each square, then place the beef on top. Wrap the pastry around the beef and seal the edges.
Place the wrapped fillets on a baking sheet lined with parchment paper. Brush with beaten egg.
Bake for 25-30 minutes or until the pastry is golden brown. Let rest for 10 minutes before serving.