Beat together the apple butter, softened butter, and 1 cup of sugar until light and fluffy.
Add the egg and vanilla extract, then beat until well combined.
Add the flour, 1 teaspoon apple pie spice, baking soda, and cream of tartar. Beat just until the dough comes together.
Cover the dough and refrigerate for at least 2 hours.
When ready to bake, preheat the oven to 375°F and line a baking sheet with parchment paper.
In a small bowl, combine the remaining 1/2 cup sugar and 1 tablespoon apple pie spice.
Scoop the dough using a tablespoon or small cookie scoop. Roll each dough ball in the spiced sugar mixture, then place them on the prepared baking sheet at least 1 inch apart.
Bake for 13–15 minutes, until the bottoms are golden brown but the centers are still soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire cooling rack to cool completely.