Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Line 2 baking sheets with parchment paper. Set aside.
Filling: In a small bowl, mix together the cheeses, egg yolk, flour, sugar, vanilla and salt until smooth. Fold in the chocolate chips. Set aside.
Cut each sheet of pastry into 4 equal-sized squares. Put 4 pastry squares on each prepared baking sheet. Spoon about 2 to 3 teaspoons of the filling into the center of each piece of pastry. Fold 1 corner of the pastry diagonally over the filling to within 1-inch of the opposite corner. Using a pastry brush, brush the folded-over section lightly with the beaten egg. Fold the opposite corner over the egg-brushed pastry to form an open-ended Danish. Brush the pastry with beaten egg and bake until puffed and golden, about 15 minutes. Remove from the oven and cool for 5 minutes before serving.
Recipe courtesy of Giada De Laurentiis