In a large saucepan over medium heat, melt the butter until it turns golden brown, about 8 minutes. Remove from heat. Strain the butter and pour it into the bowl of a stand mixer fitted with the paddle attachment. On medium-low speed, beat the butter for 5 to 7 minutes until it cools to room temperature.
In a large bowl, combine the flour, cream of tartar, baking soda, salt and 1 teaspoon cinnamon. In a small bowl, whisk together the eggs and milk.
Add 1 cup granulated sugar and the brown sugar to the butter and mix for 2 minutes on medium speed. Use a spatula to scrape down the sides of the bowl and beat in the egg-mixture on low speed. Increase the speed to medium and mix until fully combined, about 30-45 seconds.
Add the flour mixture in 3 additions mixing until just combined. Form the dough into a rough ball in the bowl and cover with plastic wrap. Chill in the refrigerator for at least 1 hour up to 24 hours.
Preheat the oven to 400 degrees F. Line two sheet pans with parchment.
In a small bowl, combine the remaining cinnamon and granulated sugar. Scoop out dough by the scant 1/4 cup, roll into a ball and coat in cinnamon sugar. Transfer to the prepared sheet pans, spacing 2 inches apart. Press the dough down with the bottom of a glass, so it is about 3/8” thick. Bake 10-12 minutes, switching the sheet pans halfway through, until the cookies are golden brown and cracked on top.
Cool the cookies on the sheet pans for 10 minutes before transferring them to a wire rack to cool completely. Store in an airtight container.