Preheat oven to 400 degrees F. Line a rimmed baking sheet with parchment paper; set aside.
In a large bowl, mix together the beef, ketchup, mustard, salt, and pepper. Form the mixture into 8 equal-size patties. In a large skillet, over medium-high heat, brown the patties for 1 to 2 minutes.
On a lightly floured surface, unfold the pastry and roll out. Cut the pastry lengthwise into 4 equal strips, then cut strips in 1/2 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.
Place the mini burgers on the prepared baking sheet. Bake for 12 to15 minutes or until puffed and golden. Let stand for 5 minutes before serving.
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