Preheat the oven: Preheat your oven to 375°F and line two baking sheets with parchment paper. This keeps the cookies from sticking and helps them bake evenly.
Cream butter and sugar: In a large bowl, beat the softened butter and sugar together until pale and fluffy, about 2 minutes. This step adds air that helps the cookies stay soft.
Add eggs and vanilla: Beat in the eggs one at a time, then mix in the vanilla extract until fully combined. The mixture should look smooth and slightly glossy.
Whisk the dry ingredients: In a separate bowl, whisk together the flour, cream of tartar, baking soda and salt. This evenly distributes the leaveners so the cookies rise consistently.
Combine wet and dry: Add the dry ingredients to the butter mixture and mix on low speed or by hand just until no streaks of flour remain. Overmixing can make the cookies tough.
Chill if sticky: If the dough feels too soft to roll, chill it in the fridge for about 15 minutes. This makes shaping the dough balls much easier.
Mix the cinnamon sugar: In a small bowl, stir together the sugar and cinnamon for rolling. Set this aside next to your baking sheets.
Roll the dough balls: Scoop the dough into 1.5-tablespoon balls and roll each one between your palms until smooth. Roll each ball generously in the cinnamon sugar mixture.
Arrange on the sheet: Place the coated dough balls about 2 inches apart on the prepared baking sheets. This gives them room to spread and puff without touching.
Bake until set: Bake for 8 to 10 minutes, until the edges look set but the centers still appear slightly underdone and pale. The cookies will continue cooking on the hot pan.
Cool on the pan: Let the cookies rest on the baking sheet for 5 minutes before transferring them to a wire rack. This short rest firms up the soft centers.
Cool completely: Allow the cookies to cool completely on the wire rack before storing. They will taste best once fully set and the cinnamon sugar has firmed up on the surface.