Preheat oven to 375F degrees. Line two large cookie sheets with parchment paper or silicone baking mats. Set aside.
Toss sugar with cinnamon in a small bowl. Set aside.
In a large bowl using a hand-held mixer or stand mixer with paddle attachment, cream the softened butter for about 1 minute on medium speed. Get it nice and smooth, then add the sugar on medium speed until fluffy and light in color. Mix in egg and vanilla. Scrape down the sides as needed. Set aside.
In a medium size bowl, whisk together the flour, cream of tartar, baking soda, cinnamon, and salt. With the mixer running on low speed, slowly add the dry ingredients to the wet ingredients in 3 different parts. The dough is quite thick and you may have to stir the rest by hand.
Take 1.5 - 2 Tablespoons of dough and roll into a ball. Roll the dough balls into the reserved cinnamon-sugar topping. Sprinkle extra cinnamon-sugar on top if desired. Bake cookies for 11-12 minutes. The cookies will be very puffy and soft. When they are still very warm, lightly press down on them with the back of a spoon or fork to help flatten them out. Allow cookies to cool on the baking sheet for 10 minutes and transfer to a wire rack to cool completely. Cookies remain soft & fresh for 7 days in an airtight container at room temperature.