Preheat oven to 400 degrees F. Line 2 large baking sheets with parchment paper.
For filling, in a large skillet heat butter and brown sugar over medium heat until butter melts. Add apples and 1/4 cup water. Cover and cook 5 minutes. Uncover and cook 8 to 10 minutes more or just until apples are tender, stirring occasionally. Remove and cool slightly. Stir in 4 oz. of the cream cheese, the flour, and egg yolk; mix well.
On a lightly floured surface, unfold and roll out one pastry sheet to a 12-inch square. Cut into nine 4-inch squares. Spoon a rounded tablespoon of the filling into the center of each square. Brush edges of pastry squares with water. Fold each pastry in half to form a triangle. Seal edges with the tines of a fork. In a small bowl combine the beaten egg and 1 Tbsp. water. Brush half of the egg mixture over pastries. Arrange on one of the prepared baking sheets. Bake 15 minutes or until puffed and golden. Remove; cool on wire rack placed over waxed paper.
Repeat with remaining puff pastry, filling, and egg mixture to make 9 more turnovers.
In a medium bowl beat the remaining 2 oz. cream cheese with a mixer on medium until smooth. Gradually beat in powdered sugar. Beat in enough milk, 1 Tbsp. at a time, to reach a thick drizzling consistency. Transfer to a resealable plastic bag. Snip one corner from the bag. Drizzle icing over the turnovers. Serve warm or let cool.