Season the beef pieces with salt and pepper. Heat the olive oil in a skillet over medium-high heat and sear the beef on all sides until browned, about 1 minute per side. Remove the beef and set it aside to cool.
Add the mushrooms and shallot to the same skillet. Cook until the mushrooms release their liquid and it evaporates, about 5 minutes. Stir in 1 teaspoon of the thyme and remove the pan from heat.
Roll out the puff pastry and cut it into 12 squares. Spread a small amount of grainy mustard in the center of each square, then top with a spoonful of the mushroom mixture and one piece of beef.
Fold the pastry around the filling and pinch the edges to seal. Place the bites seam-side down on a baking sheet lined with parchment.
Brush the tops with the beaten egg and sprinkle with the remaining thyme. Bake at 400°F for 15 to 18 minutes until the pastry is golden.