Begin by preheating your oven to 350°F (175°C). Prepare a large mixing bowl and cream together the softened butter and sugar for about 4-5 minutes until the mixture becomes light and fluffy. Periodically scrape down the sides of the bowl to ensure everything is well incorporated.

Next, add the eggs and vanilla extract, beating for an additional 1-2 minutes until fully combined and smooth. Gradually mix in the flour, cream of tartar, baking soda, and salt. Stir until the dry ingredients are just incorporated into the wet mixture, being careful not to overmix.

In a separate small bowl, blend together the sugar and ground cinnamon.

For best results, if time permits, wrap the dough in plastic wrap and chill it in the refrigerator for 20-30 minutes. Once chilled, roll the dough into small, smooth balls. Drop each ball into the cinnamon-sugar mixture, thoroughly coating it. To ensure a rich coating, use a spoon to toss the dough balls a second time in the cinnamon-sugar mixture.

For a flatter snickerdoodle, gently press down in the center of each dough ball before placing it on a baking sheet lined with parchment paper. This technique helps prevent the cookies from puffing up too much in the center.

Bake the cookies for 9-11 minutes, or until the edges are set but the centers are still soft. Allow them to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.