Preheat oven to 400F degrees.
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 the puff pastry rectangles on a large, ungreased cookie sheet leaving at least 1 inch of space between each rectangle.
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 allows the outside border to rise and puff up while the center stays lower and holds the filling.
In a small bowl, combine the cream cheese, 2 tablespoons of the sugar, and the vanilla extract. Spoon equal amounts of the filling into the center of each pastry rectangle. Spread it onto the dough within the inside border.
In a small bowl, toss the fresh blueberries with the lemon juice, then sprinkle with 1 tablespoon of the sugar. Add the sugared blueberries on top of the cream cheese on the pastries.
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 400F 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 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 on a baking rack for 10 minutes. Drizzle the frosting over the danishes.