Step 1

Place 1 stick unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place 1 large egg on the counter. Let both sit at room temperature until the butter is softened, about 1 hour.

Step 2

Place 2 1/4 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon ground cinnamon, and 1/4 teaspoon grated fresh or ground nutmeg in a medium bowl. Whisk to combine.

Step 3

Add 3/4 cup packed light or dark brown sugar and 1/4 teaspoon kosher salt to the bowl with the butter. Beat with the paddle attachment (or with electrix mixer beaters) on high speed until light and fluffy, 2 to 3 minutes. Scrape down the sides of the bowl. Add the egg, 1/2 cup applesauce, and 2 teaspoons vanilla extract, and beat on low speed until combined (the mixture will look curdled).

Step 4

Scrape down the sides of the bowl. With the mixer on the lowest speed, gradually add the flour mixture and beat just until combined with no streaks of flour remaining, about 45 seconds total. The dough will be sticky.

Step 5

Cover and refrigerate for at least 30 minutes or up to 1 hour. Meanwhile, arrange 2 oven racks to divide the oven into thirds and heat the oven to 375°F. Line 2 rimmed baking sheets with parchment paper or silicone baking mats.

Step 6

Scoop 1 1/2 tablespoon-portions of the dough and place on the baking sheets about 1 1/2 inches apart, 12 cookies per sheet.

Step 7

Bake for 5 minutes. Rotate the baking sheets from top to bottom and front to back. Continue to bake until the tops look dry and light golden-brown on bottom, 4 to 8 minutes more. Let cool on the baking sheets for 5 minutes. Transfer the cookies to wire racks and let cool completely.