Preheat the oven to 400°F (205°C) and line a large baking sheet with parchment paper.
In a large bowl, combine the ground beef, mushrooms, mustard, Worcestershire sauce, garlic, onion powder, smoked paprika, thyme, salt, and black pepper. Mix gently just until everything is evenly distributed. Avoid overworking the meat.
Lightly flour your work surface and unfold the puff pastry sheets. Roll each sheet slightly to smooth the folds and create an even rectangle.
Cut each sheet into small squares, approximately 3 to 4 inches wide, depending on how large you want the bites.
Place about 1 to 1 1/2 tablespoons of beef filling in the center of each pastry square. If using cheese, tuck a small cube into the center of the beef.
Fold the pastry around the filling and pinch the edges firmly to seal. You can form little parcels, rectangles, or triangles depending on your preferred look.
Arrange the bites seam-side down on the prepared baking sheet, leaving a little space between each one.
Brush the tops lightly with egg wash.
Use the tip of a sharp knife to make a tiny vent in the top of each pastry.
Bake for 20–25 minutes, or until the pastry is deeply golden and the beef is cooked through.
Let the bites rest for about 5 minutes before serving.