Preheat the oven to 400 degrees F.
Allow the puff pastry to come to room temperature.
Cut the puff pastry into six squares.
Divide the goat cheese among the puff pastry squares and spread evenly.
Spoon a tablespoon of fruit preserve over the goat cheese.
Fold the corners and edges of the puff pastry together. Place on a cookie sheet and bake in the oven until golden brown, about 20 minutes. Cool on a rack.
While the puff pastry is baking, prepare a glaze of with the confectionery sugar, water and almond or vanilla flavoring. Spoon the glaze over the Danish and serve immediately.
