Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until shimmering. Season beef tenderloin cubes with salt and pepper, then sear for 2-3 minutes, turning to achieve a nice brown crust. Remove from the skillet and set aside to cool.

In the same skillet, add another tablespoon of olive oil if needed and reduce the heat to medium. Sauté finely chopped mushrooms, shallots, and garlic for 5-7 minutes until golden. Add fresh thyme and season with salt and pepper before transferring to a bowl to cool slightly.

On a lightly floured surface, roll out the puff pastry until it's about 1/8 inch thick. Cut the pastry into 3x3 inch squares.

Take a square of puff pastry and place a spoonful of the mushroom mixture in the center. Add a piece of the seared beef on top. Optionally brush the beef with Dijon mustard. Fold the corners of the pastry over the filling, pinching them together to seal.

Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper, placing the assembled bites on it. Brush the tops with a beaten egg. Bake for 15-20 minutes until golden brown.

Once baked, remove from the oven and let them cool slightly. Serve warm with your favorite dipping sauce.