Mix flour and sugar in a large bowl. Cut in cold, cubed butter until the texture looks like coarse crumbs. Gradually stir in cold water (1 tbsp at a time) until the dough forms. Shape into a disk, wrap, and chill for 30 minutes.

Preheat oven to 375°F (190°C). Roll dough on a floured surface to about ⅛ inch thick, aiming for a rectangle.

Cut dough into 3x4-inch rectangles. Spoon 1 tsp blueberry preserves onto the center of half the pieces, leaving space at the edges.

Brush edges with beaten egg. Top with another rectangle. Press edges gently and crimp with a fork to seal.

Place tarts on a parchment-lined baking sheet. Brush tops with egg wash. Bake for 25–30 minutes until golden brown.

Cool on the tray 5 minutes, then transfer to a rack. Mix powdered sugar, milk, and vanilla until smooth, and drizzle over cooled tarts.