Preheat oven to 375 degrees. Line two cookie sheets with parchment paper and set aside
Make the brown butter: melt 1 stick of butter in small saucepan. Continue to melt, swirling around, until mixture starts to foam up and you see small brown specks. The butter will start to smell nutty. Immediately remove from heat, transfer to a small bowl and set aside to cool.
Whisk together the flour, cream of tartar, baking soda, spices, and salt together in a medium bowl.
In your stand mixer with a paddle attachment (or in a large bowl with a hand mixer), beat the remaining 1 stick of butter along with the cooled brown butter and granulated sugar on medium high speed until smooth and creamy, about 2 minutes.
Add the egg and vanilla extract. Beat on medium speed until combined, scraping down the sides and bottom of the bowl with a rubber spatula as needed.
Slowly add the dry ingredients in 3 stages, and mix just until combined.
To Make the Rolling Sugar: combine the granulated sugar and cinnamon together in a small bowl.
Roll cookie dough into 1" balls, and then roll in the cinnamon-sugar topping. Place about 3" apart on cookie sheets.
Bake cookies for 10 minutes, rotating half way in between. While they are still very warm, gently press down on them with the back of a spoon or fork to help flatten them out.
Allow cookies to cool on the cookie sheets for 5 minutes before transferring to cooling rack.
Store in airtight container and keep room temperature for up to 1 week. Or, place in freezer for up to 3 months.