Step 1: Prepare the Dough

1. In a large mixing bowl, whisk together the flour, sugar, and salt.
2. Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs.
3. Gradually add ice water, one tablespoon at a time, mixing until the dough comes together. Be careful not to overwork the dough.
4. Shape the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Step 2: Make the Blueberry Filling

1. In a medium bowl, combine the blueberries, sugar, cornstarch, lemon juice, and vanilla extract.
2. Gently mix until the blueberries are evenly coated. Set aside.

Step 3: Assemble the Cookies

1. Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
2. On a lightly floured surface, roll out the chilled dough to about ¼-inch thickness.
3. Use a cookie cutter to cut out circles from the dough.
4. Place half of the circles on the prepared baking sheet. Spoon a small amount of blueberry filling onto each circle, leaving a small border around the edges.
5. Use a small cookie cutter or knife to cut shapes (like hearts or stars) out of the remaining dough circles. Place these on top of the filled circles to create a “window” effect.
6. Press the edges gently to seal.

Step 4: Add the Topping

1. In a small bowl, whisk together the egg and milk to create an egg wash.
2. Brush the tops of the cookies with the egg wash and sprinkle with coarse sugar.

Step 5: Bake and Cool

1. Bake the cookies for 18-20 minutes, or until the edges are golden brown.
2. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a cooling rack.