Start by preheating the oven to 400 degrees Fahrenheit. Then unfold the puff pastry sheets and lay out on a flat surface. Use a knife to cut along the fold marks to create three equal sized strips. Cut each strip in half to make a total of 12 rectangles.
Arrange these rectangles on a large, ungreased cookie sheet leaving at least 1 inch of space between each. With a paring knife, lightly score a border around the entire edge of each pastry rectangle, about ¾ inch away from the edge. Use a fork to poke a few holes into the center area of each pastry. This process allows the outside border to rise and puff up while the center stays shorter and holds the filling.
To make the filling, combine the cream cheese, sugar, and vanilla extract in a small bowl. Spoon equal amounts of the filling into the center of each pastry rectangle. Spread it onto the dough inside border you created above. They should look something like the image below.
Sprinkle each one with some of the semi-sweet chocolate chips.
In a small bowl, beat the egg and water together. Use a pastry brush to apply a thin layer of the egg wash to the outside border of each pastry. Discard any leftover egg mixture. Bake the pastries at 400 for 18 minutes, until the danishes are golden brown.
In a small bowl, combine the powdered sugar and heavy cream (milk can be substituted for cream, but it will make the frosting thinner). The consistency should be somewhat thick, but still thin enough to drizzle. If the consistency is too thick, add a little more cream; if too thin, add more powdered sugar. Cool the danishes for about 10 minutes then drizzle the frosting over the top.
Serve this delectable treat up to your family! They will love a fresh from the oven cream cheese danish for breakfast or anytime of the day!