Place the cream cheese and sugar in a bowl and beat with an electric mixer on low speed until smooth. Add the egg yolk, almond extract and vanilla extract and mix until just combined. Set the filling aside.
Defrost the puff pastry overnight in the refrigerator (or according to the package directions). Unroll the defrosted puff pastry and place on a flat surface. Cut the 10x10 inch sheet into quarters.
Place about 1 1/2 tablespoons of the filling into the middle of each of the 4 squares. Brush the border of each pastry with egg wash.
Fold two opposite corners to the center, brushing and overlapping the corners of each pastry so they firmly stick together. Brush the top of the pastries with egg wash.
Preheat oven to 400 degrees F. Line a baking sheet with parchment paper. Place the pastries on the prepared baking sheet. Repeat with the second sheet of puff pastry and refrigerate the filled Danish for 15 minutes.
Bake the puff pastries in the oven for about 20 minutes, rotating the pan once during baking, until puffed and golden brown. Remove the stuffed pastries from the oven and cool completely on a wire rack. Serve warm or cold.