In a stand mixer fitted with the paddle attachment, cream the unsalted butter, granulated sugar, and light brown sugar together on medium-high speed until light and fluffy, about 3 minutes.
Add the egg and vanilla extract to the creamed mixture and beat on medium-high speed until combined and fluffy, about 3 minutes.
Reduce the mixer speed to low and add the all-purpose flour, baking soda, cream of tartar, and salt if using. Mix until just combined, about 1 minute.
Using a 2-inch cookie scoop or your hands, form about 14 equal-sized dough balls, flatten them slightly, and place on a large plate or tray.
Cover the dough balls and refrigerate for at least 1 hour to chill. Do not bake unchilled dough to prevent spreading.
Preheat the oven to 350°F (177°C) and line a baking sheet with a Silpat or spray with cooking spray.
Mix the 0.25 cup granulated sugar with ground cinnamon in a small bowl to create the cinnamon sugar coating.
Roll each chilled dough ball in the cinnamon sugar until fully coated.
Place the coated dough balls on the prepared baking sheet spaced at least 2 inches apart and bake for about 9 minutes until edges are set and lightly golden but centers are still soft and glossy.
Allow the cookies to cool on the baking sheet for about 10 minutes before transferring to a cooling rack or serving.
Notes
For best results, chill the dough thoroughly and avoid overbaking to keep the cookies soft and pillowy.