Cream together the butter and 1 1/2 cups sugar in a stand mixer until smooth, about 2-3 minutes.
Add the eggs, making sure to scrape down the sides of the mixing bowl. Add the flour, cream of tartar, salt and baking soda and mix on low until everything is incorporated. Cover the dough with plastic wrap and refrigerate for at least 2 hours.
Preheat your oven to 400 degrees
Combine the remaining 1/4 cup of sugar and cinnamon in a small bowl. Scoop out 2 tablespoons worth of dough and roll the dough into a ball and roll into the sugar. Place the cookies onto a parchment lined baking sheet, about 12 per sheet, and bake for 9-10 minutes until the edges are just slightly golden brown and the center is still a bit soft.
Remove the baking sheet from the oven and let the cookies rest for about 5 minutes before transferring them to a cooling rack. Repeat this process for the remaining dough.