In a mixing bowl, combine chopped pecans, brown sugar, corn syrup, beaten egg, vanilla extract, and salt. Mix well until combined.

Set the filling aside to allow the flavors to meld.

Preheat the oven to 350°F (175°C).

Roll out the puff pastry sheet on a lightly floured surface to about 1/8 inch thick.

Use a cookie cutter to cut out circles of pastry, about 3 inches in diameter.

Place the pastry circles onto a baking sheet lined with parchment paper.

Spoon a small amount of the pecan filling into the center of each pastry circle.

Fold the pastry over the filling to create a half-moon shape and press the edges to seal.

Brush the tops with the egg wash made from beaten egg and water.

Bake in the preheated oven for 20-25 minutes or until golden brown.

Remove from the oven and let cool slightly before serving.