Melt butter in a small saucepan over medium low heat. Continue to cook, stirring occasionally, until butter turns deep brown. Watch it close to make sure it doesn't brown. Remove from heat, transfer to a bowl, and chill in the fridge until solid. When ready to make the cookies, remove butter from fridge and let it come to room temperature for 20-30 minutes.
Preheat 350° F. Line a sheet pan with parchment paper.
In the bowl of a stand mixer fitted with a paddle attachment, or in a bowl with a hand-held mixer, beat the butter, granulated sugar, and brown sugar on medium high speed until light and creamy. Add the eggs, one at a time, mixing after each. Then add the vanilla.
In another bowl, combine the flour, cream of tartar, baking soda, and salt. Add to the mixer and mix until combined.
Combine sugar with the ground cinnamon to make cinnamon-sugar mixture. Portion the dough into rounded tablespoons for small cookies, or use a large 3 Tbsp cookie scoop for larger cookies. Roll dough balls in the cinnamon sugar.
Place on the prepared sheet pan. Bake for 7-9 minutes for small cookies, 10-11 minutes for larger cookies. Let cool on the pan for 5 minutes, then transfer to a cooling rack to cool completely.
Store tightly in an airtight container at room temperature for up to 3 days.