1) Preheat oven to 200 degrees C/Gas 6. Line a rimmed baking tray with greaseproof paper; set aside.
2) In a large bowl, mix together the beef, tomato ketchup, mustard, salt, and pepper. Form the mixture into 8 equal-size patties. In a large heavy saucepan, over medium-high heat, brown the patties for 1 to 2 minutes.
3) On a lightly floured surface, unfold the pastry and roll out. Cut the pastry lengthwise into 4 equal strips, then cut strips in half crosswise. Place 1 patty on each strip and top with cheese. Fold the pastry up around the burgers and pinch the edges together to seal, molding to fit around the patties. Brush the tops of the pastries with the egg mixture.
4) Place the mini burgers on the prepared baking sheet. Bake for 12 to 15 minutes or until puffed and golden. Let stand for 5 minutes before serving.