Sear the beef by heating olive oil in a skillet over medium-high heat. Season beef cubes with salt and pepper, and sear them for about 2-3 minutes per side until nicely browned. Remove from skillet and allow to cool.

Prepare the mushroom duxelles by cooking chopped mushrooms, shallots, and minced garlic in the same skillet over medium heat for 5-7 minutes until golden brown. Add thyme, salt, and pepper, then transfer to a bowl to cool.

Roll out the puff pastry on a floured surface to 1/8 inch thick. Cut into 3x3 inch squares and keep them separate.

Assemble the bites by placing mushroom duxelles in the center of each pastry square, topping with a piece of cooled beef. If using, spread a thin layer of Dijon mustard on the beef. Fold and seal the pastry edges with a fork.

Preheat the oven to 400°F (200°C). Arrange assembled bites on a parchment-lined baking sheet, ensuring they are spaced apart.

Before baking, wash the tops of each bite with beaten egg. Bake for 15-20 minutes until pastry is puffed and golden brown.

Cool slightly on the baking sheet before serving warm to guests.