Preheat your oven to 450 degrees.
On a lightly floured surface, cut the puff pastry into six equal portions.
Roll each portion into a 6×6-inch square.
Cut each log of goat cheese into three equal portions.
Arrange each portion of goat cheese onto the center of a pastry square.
Brush the edges of the pastry with the beaten egg.
Draw the sides of the pastry up to form a pyramid, pressing the edges together halfway up the sides.
Tuck a sprig of basil into the center of each tart.
Arrange the tarts on a baking sheet lined with parchment paper.
Bake for about 15 minutes or until the cheese softens and the pastry is golden brown and puffed.
Serve warm from the oven.
