Lay a piece of parchment paper out on the counter, and place one unfolded sheet of puff pastry on top. Lightly roll out the puff pastry. Place the parchment paper and puff pastry on a rimmed baking sheet.
In a medium bowl, mix together 4 ounces of cream cheese and 2 tablespoons sugar. Spread the cream cheese mixture into the center of the puff pastry, leaving a 1-inch border around the outside.
Without unfolding the second sheet of puff pastry, put it into strips about 1-inch wide.
In a separate medium bowl, mix the blueberries, remaining 2 tablespoons sugar, and cornstarch. Pour the blueberry mixture over the cream cheese filled puff pastry.
Fold up each side of the puff pastry over about 1-inch of the blueberry filling. Lay the strips of cut puff pastry over the top in a pretty pattern. Sprinkle the top of the pastry with turbinado sugar.
Bake at 375° F for 22-27 minutes, or until golden brown and puffy.
While the pastry is baking, make the cream cheese icing. Mix powdered sugar, 4 ounces cream cheese, and milk, adding milk 1 tablespoon at a time until it reaches the desired consistency. Stir until smooth.
Carefully remove blueberry breakfast pastry from the oven, and drizzle with cream cheese icing. Garnish with additional turbinado sugar if desired. Enjoy!