Preheat your oven to 375°F. Line two large baking sheets with parchment paper.
In a large bowl with a hand mixer (or stand mixer with paddle attachment), beat the butter and sugar until light and fluffy, 2 minutes. Beat in the eggs one at a time until smooth.
In another bowl, whisk the flour, cream of tartar, baking soda, and salt together. Slowly mix in the dry ingredients into the wet mixture until a thick dough forms.
Roll the dough into 1 ½-inch balls, then roll in a bowl of cinnamon sugar. Arrange on the baking sheet, about 2 inches apart.
Bake for 9–11 minutes, until the edges are set. Remove the sheet from the oven and immediately tap on the counter until the cookies deflate slightly (this is what makes them chewy!)
Cool for 5 minutes on the sheet, then transfer to a wire rack to cool completely.
Nutrition information is calculated using an ingredient database and should be considered an estimate.