Add the butter to a medium skillet set over medium heat and let it start melting. Continue cooking, swirling the pan occasionally, until the butter becomes golden brown and smells nutty (be patient and watch carefully, it can go from brown to burnt quickly). Pour the butter into the bowl of a stand mixer fitted with the paddle attachment. Mix on medium-low speed for 5-7 minutes to cool the butter to room temperature (or alternatively, you could just let it sit until it cools down - it'll just take longer).

Meanwhile, whisk the flour, cream of tartar, baking soda, 1 teaspoon of the cinnamon and the salt together in a medium bowl. Whisk the eggs and milk in a medium measuring cup until combined.

When the butter has cooled, add 1 cup of the granulated sugar and the brown sugar to the bowl. Beat on medium speed for 2-3 minutes, scraping down the sides of the bowl as necessary. With the mixer on low, slowly add the egg mixture beating until well combined. With the mixer on low speed, add the dry ingredients in 3 additions, beating just until the dough comes together. Cover the bowl and chill the dough in the refrigerator for at least 1 hour or up to 24 (I chilled mine for close to 24).

When you're ready to bake, preheat oven to 400 F. Line two baking sheets with parchment. Add the remaining 3 tablespoons of sugar and the remaining 4 teaspoons of cinnamon to a wide, shallow bowl and stir to combine.

Using a small cookie scoop (about 2 tablespoons), portion the dough into balls. Roll the balls in the cinnamon-sugar mixture then transfer to the prepared baking sheets spacing the cookies about 1 1/2-2 inches apart. Bake for about 10 minutes (rotating the pans halfway through) until the tops of the cookies are cracked and the edges are just set (just a minute or two of extra baking will take these from chewy to more crisp so keep an eye on them). Transfer the pans to wire racks and cool the cookies for a few minutes then remove to the racks to cool completely. Store in an airtight container at room temperature.