Prep: Preheat the oven to 375F. Line two baking sheets with parchment paper or silicone baking mats and set aside. Make the topping by mixing the cinnamon and sugar together in a small bowl; set aside.
Cream the Butter: Add the softened butter and sugar to a large bowl. Use a hand mixer or stand mixer to cream the butter and sugar together until smooth, about 1 to 2 minutes. Add the milk and vanilla and mix again until well combined.
Dry Ingredients: Add the flour, cornstarch, cream of tartar, baking soda, salt, and cinnamon to the bowl. Use a spatula to mix the dry ingredients together, then incorporate them into the butter mixture to form a dough. The dough may look slightly dry, but should stick together when you pinch it. If the dough is too dry add more milk in 1 tbsp increments.
Make the Cookies: Use a cookie scoop or tablespoon to divide the dough into 2-tablespoon sized balls. Roll the cookie dough together to form a smooth ball, then roll each ball in the cinnamon sugar topping and place 2 inches apart on the baking sheet. Lightly flatten each cookie dough ball onto the sheet as they will not spread much when baking. (Note: if you want your cookies extra thick, don’t flatten them!)
Bake: Bake for 9 minutes; the cookies will appear puffy and soft. Let the cookies cool on the baking sheet for 10 minutes, then transfer them to a wire rack and let them cool completely.
Storage: Store the cookies in an airtight container at room temperature for up to 5 days. You can also freeze the cookies (or cookie dough!) for up to 2 months.
Cornstarch can be replaced with arrowroot powder.
Vegan butter can be replaced with softened coconut oil. I recommend using refined coconut oil, as it has no coconut flavor.