Preheat oven to 350 degrees F and line baking sheet(s) with parchment paper.
In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter, 1 cup of the sugar, and brown sugar on medium high speed until light and creamy. Add the eggs and beat to combine, scraping the bowl down as necessary.
In a separate bowl, combine the flour, cream of tartar, baking soda, salt, and 1/2 teaspoon of cinnamon. Add to the the stand mixer and mix on medium speed until combined.
Combine the remaining sugar and cinnamon in a small bowl. Roll the cookie dough into rounded tablespoons and roll in the cinnamon sugar. Place evenly on the prepared cookies sheets.
Bake until they are puffed and slightly cracked, about 9-11 minutes. Cool on a wire rack.
Cookies will keep in an airtight container at room temperature for several days.