Preheat your oven to 350 degrees Fahrenheit.
In a big mixing bowl, cream together softened butter and sugar until it’s light and fluffy, about 4-5 minutes. Scrape the sides, then add eggs and vanilla, and continue to cream for another 1-2 minutes.
Stir in the flour, cream of tartar, baking soda, and salt, mixing just until everything is combined.
In a small bowl, combine sugar and cinnamon for the coating.
For an extra touch, refrigerate the dough for 20-30 minutes if time allows. Roll the dough into small, round balls, and coat them generously in the cinnamon-sugar mixture. Use a spoon to coat them a second time, ensuring the cookies are fully covered.
If you prefer flatter snickerdoodles, press down in the center of each ball before placing them in the oven. This prevents them from puffing up too much.
Arrange the coated dough balls on a parchment paper-lined baking sheet. Bake for 9-11 minutes.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack.