Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a bowl, whisk together the flour, baking soda, cream of tartar, and salt.
In another bowl, cream the softened butter and sugar until smooth and fluffy.
Add the egg yolk, vanilla extract, and milk to the butter mixture, and mix until well combined.
Gradually add the dry ingredients to the wet mixture, stirring until a soft dough forms.
In a small bowl, combine the sugar and cinnamon for rolling.
Roll the dough into 12 equal balls, then roll each ball in the cinnamon-sugar mixture.
Place the balls on the baking sheet, spacing them out slightly. Gently flatten each cookie with your hand or the back of a spoon.
Bake for 10-12 minutes, or until the edges are set and the cookies are slightly puffed. Let them cool on the baking sheet for a couple of minutes before transferring to a wire rack to cool completely.