In large mixing bowl, use a hand mixer (or stand mixer with paddle attachment) to beat together the butter, sugar, and brown sugar until combined. Add the egg and vanilla and beat until smooth.
In another bowl, stir together the flour, salt, baking soda, and cream of tartar until well combined.
Add the dry ingredients into the wet ingredients and stir just until combined and it forms a dough. Cover and refrigerate dough for at least 30 minutes.
Preheat the oven to 350°F. Cover a sheet pan with parchment paper or spray with cooking spray.
In a shallow dish, stir together the sugar and cinnamon mixture (for rolling).
For each cookie, scoop a small amount of dough out and roll into a ball. (You’re aiming for the size of a walnut or a little smaller.) Roll cookies into cinnamon sugar mixture until coated and place on the sheet pan. The cookies will flatten out while they bake, so make sure to leave a little room between them. (You may have to bake two batches depending on the size of your sheet pan.)
Bake cookies for 12-14 minutes (don’t overcook them). The cookies will seem a bit undercooked, but they will continue to “carry-over cook” after they are removed from the oven. Let the cookies sit on the pan for 5-10 minutes until they firm up a bit and then carefully transfer to a cooling rack.