Heat a skillet over medium-high heat and add olive oil. Season the beef cubes with salt and pepper. Sear beef for 2-3 minutes on each side until browned but still rare. Remove and cool.

In the same skillet, add chopped mushrooms, shallots, and garlic. Cook for 5-7 minutes until mushrooms are golden and moisture evaporates. Add thyme, season, and mix well. Transfer to a bowl to cool.

On a floured surface, roll out puff pastry to 1/8 inch thick. Cut into 3x3 inch squares and refrigerate.

Place a spoonful of mushroom duxelles on each pastry square, followed by a piece of seared beef. Brush with Dijon mustard if desired. Fold corners of pastry over filling and seal with a fork.

Preheat oven to 400°F (200°C). Arrange assembled bites on a parchment-lined baking sheet and brush tops with beaten egg. Bake for 15-20 minutes until pastry is puffed and golden.

Let bites cool on the baking sheet for 5 minutes before serving. Enjoy warm with horseradish sauce or mustard.