Apple Pie Cookies

Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

Beat butter in a large bowl with an electric mixer at medium speed for 30 seconds. Beat in 1 cup sugar and baking powder until combined, scraping sides of bowl as needed. Beat in 1 egg, the vanilla, and salt. Beat in as much of the 3 1/2 cups flour as you can with the mixer. Stir in any remaining flour. Divide dough in half.

Turn one dough half out onto a lightly floured surface; roll to 1/8-inch to 1/4-inch thickness. Cut out 3-inch circles with a round or apple-shaped cutter. Repeat with remaining dough half, rerolling scraps as needed.

Stir together chopped apple and apple butter in a small bowl. In another small bowl, whisk together remaining egg and 1 tablespoon water.

Brush half of the cookies lightly with half of egg wash. Spoon a generous 1 teaspoon apple filling onto the center of each egg-washed cookie. Top with remaining cookies, pressing edges to seal. Lightly brush cookie tops with remaining egg wash. Use a sharp knife to cut small slits in cookie tops to vent. Using a spatula, carefully transfer 6 filled cookies onto each prepared baking sheet.

Bake in the preheated oven, in batches as needed, until golden brown, 20 to 24 minutes. Cool on pans about 5 minutes.

Meanwhile, stir together remaining 1/2 cup sugar and the cinnamon in a shallow dish. Carefully dredge warm cookies in the sugar mixture until coated. Gently tap off excess. Transfer cookies to a wire rack to cool, about 10 minutes. (To store, chill cookies in an airtight container up to 1 week.)