Preheat oven to 375 degrees. Line baking sheets with parchment paper.
In the bowl of a stand mixer, beat butter and shortening on medium-high speed for 1 minute, until smooth and creamy. Add sugar and beat until fluffy. Add eggs, mixing after each addition, then milk and vanilla.
In a medium bowl, whisk together flour, soda, cream of tartar, salt and cinnamon.
While mixer is set to low speed, slowly add dry ingredients to butter mixture. Mix until combined.
Remove bowl from mixer and chill dough for 30 minutes. Once dough is sufficiently chilled, use a standard cookie scoop to create balls. Roll dough in hands to form balls, then roll into cinnamon sugar mixture. Place onto cookie sheet and flatten slightly with the bottom of a glass cup.
Bake for 8-10 minutes, rotating the sheet half way through the baking process. Once cookies begin to brown, remove from oven (don't over cook them or they will be dry and crumbly).
Let cookies cool on sheet for 3-5 minutes before transferring them to a wire rack to cool completely.