In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and sugar with an electric mixer until light and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each. Mix in the vanilla extract.
Add the flour mixture to the wet ingredients in two additions, mixing on low speed until just combined. Cover the dough and refrigerate for 30 minutes. Chilling firms the dough and results in thicker, chewier cookies.
Preheat your oven to 375F (190C). Line two baking sheets with parchment paper. In a small bowl, mix together the 3 tablespoons of sugar and 2 teaspoons of cinnamon.
Scoop generous tablespoon-sized portions of dough and roll each into a ball. Roll each ball in the cinnamon sugar mixture until evenly coated, then place them on the prepared baking sheets about 3 inches apart.
Bake for 9 to 11 minutes, until the edges are just set but the centers still look slightly underdone and puffy. They will flatten and firm up as they cool.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack. They will be perfectly soft and chewy in the center with slightly crinkled tops.