Start by heating a tablespoon of olive oil in a skillet over medium-high heat. Season the beef tenderloin with salt and pepper, then sear for 2-3 minutes on each side until browned but not fully cooked. Remove the beef and let it cool.

In the same skillet, add another drizzle of olive oil and sauté finely chopped mushrooms, shallots, and garlic over medium heat for 5-7 minutes until golden brown. Stir in fresh thyme and season, then let cool.

Roll out the chilled puff pastry on a floured surface to 1/8 inch thick. Cut into 3x3 inch squares, covering with a damp cloth to prevent drying.

Take one square of pastry, add a spoonful of cooled duxelles, and sliced seared beef on top. Add Dijon mustard if desired. Fold pastry corners over and seal edges with a fork.

Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper. Place assembled bites on the sheet, brush tops with beaten egg, and bake for 15-20 minutes until golden brown.

Remove from oven, let cool slightly on a wire rack, and serve warm, optionally with creamy horseradish sauce or mustard for dipping.