Heat berries, sugar and lemon juice on the stovetop in a medium-sized saucepan on low heat for abut ten minutes or until the berries start releasing their juices, stirring frequently. Once there is a lot of juice, mix cornstarch and water together and stir into the blueberry mixture. Bring to a gentle boil and simmer for 2-3 minutes, stirring constantly until thickened. Cool filling until warm to the touch before filling dough.
Take your puff pastry sheet and cut it into 6 equal squares. Distribute filling evenly in the center of each square. Whisk egg and water together in a small bowl and brush on the edges of the dough before folding over into a triangle shape and pinching the edges closed with a fork. The filling might squish out a little bit, but that's okay. Brush the tops of the triangles with more egg wash and sprinkle tops with sugar.
Preheat oven according to puff pastry's manufacturer's instructions and bake for 15-20 minutes or until light golden brown. Allow them to cool slightly. Prepare glaze while they are cooling. Whisk confectioner's sugar, vanilla and cream or milk together until smooth. Drizzle over warm pastries.
Blueberry Turnovers will stay fresh for up to 3 days stored in an airtight container at room temperature. To crisp them up again, place in a toaster oven for a few minutes and they are good as new!