Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Heat olive oil in a skillet over medium-high heat. Sear beef cubes on all sides, about 1-2 minutes total. Remove and let cool.
In the same skillet, melt butter and sauté mushrooms, shallot, thyme, salt, and pepper until mixture is dry. Set aside to cool.
Roll out puff pastry on a floured surface and cut into 3-inch squares.
Brush each beef cube with Dijon mustard. Top with mushroom mixture and place on puff pastry square.
Wrap pastry around beef and seal edges. Place seam-side down on baking sheet.
Brush tops with egg wash and bake for 15-20 minutes or until golden brown.
Let rest for 5 minutes before serving.