Whisk the flour, baking soda, and kosher salt together in a medium bowl.

Beat the softened butter, peanut butter, granulated sugar, and packed light brown sugar until light and fluffy, about 2–3 minutes.

Beat in the egg and vanilla extract, then gradually mix in the dry ingredients just until the dough is combined.

Chill the dough for about 30 minutes so it is easier to shape and less likely to spread in the oven.

Heat the oven to 350°F and line baking sheets with parchment paper.

Scoop the dough into roughly 1-tablespoon portions, roll each portion into a ball, and lightly coat it in granulated sugar.

Arrange the dough balls about 2 inches apart on the prepared baking sheets. Press a thumb or the rounded end of a measuring spoon into each ball to create an indentation.

Bake for 10–12 minutes, until the cookies are set and lightly golden at the edges. Cool them on the baking sheet for about 5 minutes, then transfer them to a rack.

If the indentations puff during baking, press them again immediately while the cookies are warm. Once the cookies have cooled slightly, fill each indentation with approximately 1 teaspoon of pumpkin butter.