Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the peaches into thin wedges and toss them with sugar, lemon juice, cinnamon, and flour.
Mix the softened cream cheese, sugar, vanilla, and flour until smooth.
Cut the thawed puff pastry into 8 equal pieces and place them on the prepared baking sheet.
Spoon cream cheese filling into the center of each pastry.
Arrange peach slices over the cream cheese.
Whisk the egg with water and brush the pastry edges with the egg wash.
Bake for 18–22 minutes, or until puffed and golden brown.
Cool for several minutes.
Whisk together the powdered sugar, milk, and vanilla, then drizzle over the cooled pastries if desired.
Serve warm or at room temperature.