Prepare the Dough

1. Preheat Oven: Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
2. Make the Dough: In a large bowl, combine the flour, salt, and sugar. Add the cold, cubed butter and use a pastry cutter or your fingers to mix until the dough resembles coarse crumbs. Slowly add ice water, 1 tablespoon at a time, and mix until the dough just comes together.
3. Chill the Dough: Wrap the dough in plastic wrap and refrigerate for 15-20 minutes to chill.

Prepare the Blueberry Filling

1. Cook the Filling: In a medium saucepan, combine the blueberries, sugar, cornstarch, cinnamon, lemon juice, and vanilla extract. Cook over medium heat, stirring occasionally, until the mixture thickens and the blueberries burst, about 5-7 minutes. Remove from heat and let cool to room temperature.

Assemble the Cookies

1. Roll Out the Dough: On a lightly floured surface, roll the chilled dough out to about ¼-inch thickness. Use a round cookie cutter or a glass to cut out circles (about 3 inches in diameter).
2. Fill the Cookies: Spoon a small amount of the blueberry filling into the center of each dough circle.
3. Seal the Cookies: Fold the dough over the filling to form a half-moon shape. Press the edges together with a fork to seal them, and then place them on the prepared baking sheet.
4. Bake: Bake the cookies in the preheated oven for 20-25 minutes, or until the crust is golden brown.
5. Cool: Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.

Add the Sugar Glaze

1. Make the Glaze: In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
2. Drizzle the Glaze: Drizzle the glaze over the cooled cookies for a sweet, festive touch.