Apple Pie Cookies

Pulse ¼ cup granulated sugar, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 2½ cups (313 g) all-purpose flour in a food processor to combine. Add 1 cup (2 sticks) unsalted butter, cut into small pieces, frozen 15 minutes and pulse until coarse, pea-size crumbs form, about 10 seconds. With the motor running, add 1 Tbsp. chilled apple cider vinegar and ¼ cup ice-cold water and process until dough just comes together, about 30 seconds. Squeeze a small amount of dough between your fingertips; if it’s very crumbly, add more water, 1 Tbsp. at a time (2 Tbsp. maximum). Do not overprocess.

Turn out dough onto a lightly floured surface and form into a rough ball. Knead a few times to combine, then divide into 2 equal balls. Flatten each ball into a disc with smooth edges and no cracks. Cover with plastic wrap and chill at least 1 hour or up to overnight.

Peel, core, and slice 2 medium Honeycrisp, Braeburn, and/or Golden Delicious apples (about 1 lb. total) into ¼"-thick slices. Coarsely chop slices. Transfer to a large pot and add ¼ cup light brown sugar, 2 tsp. fresh lemon juice, ½ tsp. ground cinnamon, ¼ tsp. Diamond Crystal or Morton kosher salt, 2 tsp. all-purpose flour, and 2 Tbsp. water; stir to combine. Cook over medium heat, stirring occasionally and adding more water 1 Tbsp. at a time if bottom starts to brown, until apples are softened but still have a little bite, about 10 minutes. Let cool to room temperature.

Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper. Beat 1 large egg and 1 Tbsp. whole milk in a small bowl.

Roll 1 disk of pie dough on a lightly floured surface to an ⅛"-thick round about 13" in diameter. Using 3" cutter, cut dough into 12 rounds. Transfer rounds to prepared baking sheet. Spoon 1 heaping Tbsp. filling onto each round (do not overfill). Chill on sheet until ready to use.

Roll second disk of pie dough on a lightly floured surface to an ⅛"-thick round about 13" in diameter. Using 3" cutter, cut into 12 more rounds. Using leaf-shaped cutter, cut a hole in center of each round.

Brush edges of apple-topped rounds with egg wash. Place cutout rounds over filled rounds to create sandwiches, then press down lightly around edges to seal completely. Gently press down in center to even out filling.

Brush top of sandwiches with egg wash and sprinkle with demerara sugar if using.

Bake cookies until golden brown and crisp on the bottom, 30–35 minutes. Let cool on cookie sheet 5 minutes, then transfer to a wire rack and let cool completely. Do Ahead: Cookies can be baked 2 days ahead. Loosely cover with foil and store at room temperature. Do not store in a sealed container or they will become too soft.