Make the cream cheese filling. In a large bowl, combine the softened cream cheese, sugar, egg yolk, vanilla extract, and lemon zest. Blend on high speed with an electric mixer until smooth.
Roll out puff pastry. On a lightly floured surface, roll out each sheet of thawed puff pastry until it measures 9×11 inches.
Cut each sheet. Using kitchen shears, cut off the two top corners of each sheet (set aside) and then cut 9-10 slits into each side, stopping about 1/3 of the way in from the edge. Cut off the two remaining flaps at the bottom (set aside).
Put the filling into the danish. Split the filling between the danishes, placing it in the center.
Braid the cheese danish. Starting at the top, cross the strips over each other, alternating left and right. When you get to the last two strips, just fold up the bottom flap and cross those last two strips over it. Place the danishes gently on a baking sheet lined with parchment paper.
Make the egg wash. In a small dish, combine the egg and 1 tsp. of water, mix, and brush over the tops of the danishes with a pastry brush.
Bake. Place the danishes in the oven and bake at 400 degrees Fahrenheit for 20-25 minutes, until golden brown. Then, remove them from the oven and allow them to cool to room temperature.
Make the icing. Combine powdered sugar with heavy cream and then drizzle the icing over the cooled danish.