Whisk sugar and cinnamon together in a pie plate or shallow dish.
For the Snickerdoodle Cookies
Preheat oven to 375 degrees (F).
In a medium skillet (see note), melt cubed butter on medium heat, stirring occasionally. Butter will melt, simmer and then start to foam. Once the butter starts to become foamy, it is beginning to brown. DO NOT LEAVE IT!
Check how brown it is by running a wide rubber spatula through the mixture. Once it is medium golden and has a nutty aroma, immediately transfer it into a heat-proof bowl.
Place the browned butter in the refrigerator to cool while you prep the other ingredients.
Whisk together flour, salt, baking soda, and cream of tartar.
Combine browned butter and sugar, mix until combined.
Add eggs, one at a time, beating well between each addition.
Add milk and vanilla extract, beat until combined.
Slowly add dry ingredients into the creamed mixture.
Mix until everything just comes together, scraping down the bowl as needed.
Check the consistency of the dough, you may have to add few tablespoons more flour. You should be able to touch it without it sticking too much to your fingers.
Form dough into 1-inch balls and roll in cinnamon sugar mixture.
Place 12 balls per cookie sheet and gently press a cross-hatch into the top with a fork until the cookies are flattened to about 1/2 an inch thick.
Bake for 8-12 minutes until the edges are set and the very middle still looks slightly under baked.