Preheat the oven. Set to 350°F (175°C). Line two baking sheets with parchment paper.
Whisk dry ingredients. In a medium bowl, whisk flour, cream of tartar, baking soda, salt, cinnamon, and nutmeg until evenly combined.
Cream butter, apple butter, and sugars. In a large bowl, beat the softened butter, apple butter, granulated sugar, and brown sugar on medium speed for 2–3 minutes until light and fluffy.
Add egg and vanilla. Beat in the egg and vanilla until smooth.
Scrape the bowl to make sure everything is evenly mixed.
Add dry ingredients. Mix in the flour mixture on low speed just until no dry streaks remain. The dough will be soft.
Chill the dough. Cover and refrigerate for 30–45 minutes. This helps control spread and keeps the cookies thick and chewy.
Make the coating. Stir together the granulated sugar, cinnamon, and a pinch of nutmeg in a small bowl.
Portion and roll. Scoop dough into 1 1/2-tablespoon balls (about a medium cookie scoop).
Roll each ball in the cinnamon-sugar mix to coat all sides.
Bake. Place on prepared sheets, spacing about 2 inches apart. Bake 9–11 minutes, until the edges are set and the centers look slightly underdone.
Cool. Let cookies rest on the sheet for 5 minutes, then move to a wire rack to cool completely. They’ll finish setting as they cool.