Preheat your oven to 180°C (350°F) and line a baking tray with baking paper.
In a large bowl, cream together the softened butter and sugar until light and fluffy. A hand or stand mixer works well here.
Beat in the eggs, one at a time, then stir in the vanilla extract. Make sure everything is well combined, scraping down the sides of the bowl if needed.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, and salt. Add this to the wet ingredients and mix until you have a soft, slightly sticky dough.
In a small bowl, combine sugar and cinnamon. Scoop out the cookie dough, then roll it into balls, and coat them in cinnamon sugar.
Place the coated dough balls onto your prepared tray, leaving a little space for spreading. Bake for 10–12 minutes, or until the edges are lightly golden. Don’t worry if the centres look soft, they’ll firm up as they cool.
Allow the cookies to cool on the tray for 5 minutes before transferring them to a wire rack. Enjoy warm, or let them cool completely for storing.