Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Season beef cubes with salt and pepper, sear for 2-3 minutes on each side until browned, then allow to cool.

In the same skillet, add another tablespoon of olive oil, reduce heat to medium, and sauté chopped mushrooms, shallots, and garlic for 5-7 minutes until golden brown. Stir in thyme, season, and cool completely.

Preheat oven to 400°F (200°C). Roll out puff pastry to 1/8 inch thick, cut into 3x3 inch squares, and set aside on a parchment-lined baking sheet.

Place a spoonful of mushroom duxelles on each pastry square, top with a piece of cooled beef, and brush lightly with Dijon mustard if desired. Fold pastry over, seal edges with a fork.

Arrange assembled bites on baking sheet, brush tops with beaten egg, and bake for 15-20 minutes until golden brown.

Let cool slightly, serve warm with dipping sauces like horseradish or mustard.