Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a small bowl, whisk together the 1/4 cup granulated sugar and 1 1/2 tbsp cinnamon for the coating. Set aside.
In a large bowl, cream the butter and 1 1/2 cups of granulated sugar on high speed until light and fluffy (about 3 minutes).
Beat in the eggs and vanilla extract.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, and salt.
Gradually blend the dry ingredients into the wet ingredients until a soft dough forms.
Scoop the dough into 1.5 tablespoon-sized balls. Roll each ball heavily in the cinnamon-sugar mixture until fully coated.
Place 2 inches apart on the baking sheets and bake for 9-11 minutes. The cookies will puff up and then flatten slightly, with crinkled edges.
Let cool on the pan for 5 minutes before transferring to a wire cooling rack.