Peach Cobbler Cookies

For filling: Place peaches, brown sugar, butter, vanilla, cinnamon, nutmeg, and salt to a small saucepan over medium heat. Cook, stirring frequently, until mixture is boiling and sugar is dissolved, about 5 minutes.

Stir lemon juice and cornstarch together in a small bowl until thoroughly combined; pour into the peaches and stir to thoroughly incorporate. Continue to cook, stirring constantly, until thickened, 2 to 3 minutes. Pour mixture into a heatproof container and refrigerate until thoroughly chilled, about 1 hour, or up to 2 days.

For cookie dough: Beat butter, brown sugar, 1/2 cup white sugar, salt, cinnamon, and nutmeg together with an electric mixer until light and fluffy, about 3 minutes. Add in egg, vanilla, and almond extract and beat for 1 minute more. Add in flour, baking powder, and baking soda and mix on low speed until mixture comes together in a stiff dough.

Pour remaining 1/4 cup white sugar into a small bowl and set aside. Scoop out 1 1/2 tablespoons dough and roll it into a ball. Roll dough ball in white sugar until thoroughly coated. Using your thumb or the handle of a wooden spoon or spatula, press an indentation into the center of the cookie measuring about 3/4-inch wide and about 1/3-inch deep. Repeat process with remaining cookie dough.

Remove filling from the refrigerator. Place about 1 1/2 teaspoons filling into the indentation of each cookie, heaping the filling into the center of the cookies. Refrigerate filled cookies for 30 minutes.

Preheat the oven to 350 degrees F (180 degrees C) and line baking sheets with parchment. Place cookies about 2 inches apart on the prepared baking sheets.

Bake cookies, 1 pan at a time, in the preheated oven until edges begin to turn golden brown, 15 to 20 minutes. Cool cookies on the pan for 5 minutes; remove to a wire rack to cool completely. Store cooled cookies in the refrigerator.