Preheat the oven to 400℉. Line a large baking sheet with parchment paper.
In a small bowl, combine the sugar, flour and cinnamon. Add the chopped peaches, and toss to coat.
Unfold the puff pastry on a work surface. Cut the pastry into four squares. Brush the edges of each square with milk. Evenly spoon the peach mixture onto the centers of the squares. Fold one corner of a square over the filling to the opposite corner. Press the edges with the tines of a fork to seal. Place the turnovers on the prepared baking sheet. Prick the tops of the turnovers several times with a fork. Brush with additional milk, and then sprinkle each turnover with coarse sugar.
Bake 15 to 18 minutes, or until puffed and golden brown. Cool slightly on a wire rack while you prepare the glaze.
ADD THE GLAZE:
In a medium bowl, whisk together the powdered sugar, 1 teaspoon of milk, vanilla and cinnamon. Add a little more milk, if it's too thick. Drizzle the glaze over the warm turnovers.