Preheat oven to 350°F. Line two large cookie sheets with parchment paper.
In the bowl of a large stand-mixer, cream the butter and the sugar medium speed for 4-5 minutes, or until light and fluffy (this step is always important in baking). Then, add the eggs, one at a time, and mix until combined, approximately 1 minute. Scrape down the sides of your bowl, if needed, and, with the mixer running add the vanilla. Continue to mix for an additional 1 minute.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt.
With your mixer set to low-speed, add the dry ingredients to the wet ones, and mix just until combined. Do not overmix.
Time allowing, cover your mixing bowl with plastic wrap, and refrigerate for 20-30 minutes. Not too long that the dough hardens completely, but just long enough that it will be easier to roll into small balls.
Meanwhile, combine the sugar and cinnamon in a small bowl. If you love extra cinnamon, double the total amount of cinnamon to 2 tablespoons.
Use a cookie scoop to scoop equally sized balls of dough (approximately 1 tablespoon). Roll the cookie dough balls between the palms of your hands until they are round and smooth. Carefully drop into the cinnamon-sugar mixture and roll to coat in the mixture. Transfer to your parchment-lined baking sheet.
Optional- for flatter, less fluffed up snickerdoodle cookies, gently press down in the center of each dough ball using the bottom of a glass cup just slightly.
Transfer baking sheets to your preheated oven and bake for 7-9 minutes (total cooking time will vary), or until golden around the edges. Allow cookies to rest for 5 minutes before transferring to a wire rack to cool completely.