Thaw your puff pastry dough according to package directions.
Preheat your oven to 400 degrees.
Line a baking sheet with parchment or a silicone liner.
In a small sauce pan, combine blueberries, sugar, cornstarch, and water. Stir carefully together over medium heat for 2-3 minutes until bubbling nicely and thickened. Remove from heat and let cool.
Cut pastry dough into 4 squares per sheet. Put 1-2 TBS of filling in the middle of each square.
Whisk together water and egg to create and egg wash. Brush egg wash over each edge of the pastry dough and fold in half to make a triangle. Press edges together with fingers. Pierce the top of each turnover with a fork or knife to let steam escape. Place on prepared baking sheet and repeat with remaining dough and filling. Brush remaining egg wash over the tops of turnovers.
Bake for 15-20 minutes until golden brown. Allow to cool completely.
Whisk together powdered sugar with additional glaze ingredients, add more liquid or more sugar to reach desired consistency. Drizzle glaze over each turnover and serve.