Preheat oven to 375°F degrees. Prepare two cookie sheets with parchment paper or silicone baking mats and set aside.
In a small bowl, whisk to combine ¼ cup sugar with 1 ½ teaspoons cinnamon. Set aside.
In a large bowl using a stand mixer or hand mixer, beat butter for about 1 minute on medium-high speed until smooth. Add remaining 1 ½ cups sugar and beat on high speed until pale and fluffy.
Add egg and vanilla to butter mixture and beat until combined. Set aside.
In a medium bowl, whisk together flour, cream of tartar, baking soda, the remaining 3 teaspoons of cinnamon, and salt. Add the flour mixture to the butter mixture and mix on low speed until completely combined - dough will be very thick.
Scoop out 2-3 tablespoons of dough and roll into a ball (a large cookie scoop works well). Roll in cinnamon sugar mixture and place each ball of dough on prepared pans several inches apart (they’ll spread quite a bit).
Bake for 10 minutes. Remove from oven and lightly press on the top of each cookie to flatten them a bit. Let cool on baking sheets for 5-10 minutes until they’ve set, then move to wire racks to cool completely.