Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.
In a small bowl, whisk together the flour, cream of tartar, cinnamon, baking soda, and salt. Set aside.
In a large bowl, cream the room temperature butter and granulated sugar with an electric mixer for about 1 1/2 minutes, until lighter in color and creamy. Beat in the egg and vanilla until combined.
Add the dry ingredients to the wet ingredients and beat on low speed until you have a thick, slightly sticky dough.
In a separate small bowl, stir together the granulated sugar and cinnamon for the coating.
Scoop the dough into 14 balls, around 1 1/2 tablespoons each. Roll each ball in the cinnamon sugar to coat all over.
Place the cookies on the lined baking sheets, spaced at least 3 inches (7.5 cm) apart.
Bake for around 10 minutes, until the cookies are puffy and thick with slightly crispy edges. The tops should still feel soft. The exact bake time will vary by oven.
If you want a flatter cookie, tap the tray on the counter once or twice as soon as it comes out of the oven.
Let the cookies cool on the tray for 5 minutes before transferring to a wire rack.