Preheat oven to 400 degrees F.
In a medium pot, combine the first 6 ingredients and mix well. Cook on medium heat until tender and syrupy; about 10 minutes. Allow to cool in refrigerator for 1 hour.
Roll out the puff pastry into a rectangle on a well-floured surface and cut into 8 squares. Place onto a sheet tray lined with parchment paper. Brush the edges of the square with the beaten egg. Place about 2 1/2 tablespoons of filling in the center of the square, leaving 1-inch on all sides clear. Repeat until all the puff pastry is used. Fold the turnover into a triangle and using a fork, crimp along the edges making sure to enclose all the filling in the pastry. Brush egg wash on top of each triangle.
Bake the turnovers until puffy and golden brown, about 8 to 10 minutes. Dust with confectioners' sugar.