Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the softened unsalted butter, sugar, and brown sugar. Cream together on medium speed until light and fluffy, about 2-3 minutes.
Add the large egg and vanilla extract to the creamed mixture. Beat until well combined.
In a separate bowl, whisk together the all-purpose flour, cream of tartar, baking soda, and salt. Gradually add this to the wet ingredients, mixing until just combined.
In a small bowl, combine the 1/4 cup of sugar with the 2 teaspoons of cinnamon for coating.
Using a spoon or cookie scoop, portion out the dough and roll it into balls. Roll each ball in the cinnamon-sugar mixture until fully coated.
Place coated dough balls on a baking sheet lined with parchment paper, spacing them about 2 inches apart. Bake for 10-12 minutes, until edges are set and tops are slightly cracked.
Remove from oven and let cool on the baking sheet for 5 minutes before transferring to a cooling rack.
