Heat a skillet over medium-high heat and add a splash of olive oil. Season the beef cubes with salt and pepper, then sear for 2-3 minutes on each side until a rich brown crust forms. Remove from skillet and set aside to cool.

In the same skillet, add chopped mushrooms, shallots, and minced garlic. Sauté for 5-7 minutes until mushrooms release moisture and mixture becomes golden brown. Add fresh thyme and season with salt and pepper. Allow to cool.

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

Place a spoonful of cooled mushroom mixture in the center of each square. Top with a seared beef cube and a dollop of Dijon mustard. Fold pastry over filling and seal edges firmly.

Preheat oven to 400°F (200°C). Arrange bites on a baking sheet. Brush with beaten egg and bake for 15-20 minutes until pastry is puffed and golden brown.

Remove bites from oven and let cool slightly. Serve warm with horseradish or mustard for dipping.