Preheat oven to 400 degrees Fahrenheit. Place rack in the center of oven. Line a large baking sheet with parchment paper.
In a medium bowl, beat together cream cheese, sugar, egg yolk, vanilla and lemon zest until smooth and creamy.
Place thawed puff pastry sheets on a lightly floured surface. Cut each sheet into 4 equal squares. Fold each corner of each square inward, creating an octagon shape.
Spoon about 2 tablespoons of cream cheese mixture into the center of each pastry. Press one of each berry about halfway into the filling. Trasfer pastries to baking sheet.
In a small bowl, beat together 1 egg and 1 tablespoon of water. Brush the outside of each pastry with egg wash.
Bake pastries about 15-20 minutes, or until golden brown. Remove from oven and let cool on a wire rack.
In a small bowl, whisk together powdered sugar, lemon juice and zest. Drizzle over danishes and serve.