Preheat oven to 375 degrees F. Line two large cookie sheets with parchment paper and set aside.
In a small bowl, combine ¼ cup sugar and 1 tbsp cinnamon. Set aside.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars on high speed until light and fluffy, about 2 minutes. Add the eggs and vanilla. Beat on medium-high speed until combined. With the mixer on low speed, slowly add the flour mixture. Continue mixing until a dough forms.
Form the cookies by rolling 2 tablespoons of cookie into a ball. Break in half and use your thumb to gently press into the bottom on one half. Carefully add 1 teaspoon on chilled pumpkin butter inside. Place the other cookie dough half on top and roll the dough to make a smooth ball. Roll the ball into the sugar-cinnamon and place on cookie sheet. Repeat with remaining dough.
Bake cookies for 10-12 minutes. The cookies will puffy and soft straight out of the oven. While they are still warm, gently press down on each cookie to help flatten them. Allow cookies to cool on the cookie sheet for 10 minutes before transferring to a cooling rack to cool completely.
Keep cookies in an airtight container at room temperature for up to 5 days.