Preheat your oven to 180°C (350°F) and line a baking sheet with parchment paper to prevent sticking.
In a large mixing bowl, cream together the softened butter and granulated sugar until the mixture is light, fluffy, and fragrant, about 2-3 minutes. You should see it turn pale and feel a slight resistance when you stir.
Add the eggs one at a time, mixing well after each addition, until the mixture is smooth and glossy with a subtle vanilla aroma.
Stir in the cream of tartar, baking soda, ground cinnamon, lemon zest, and a pinch of salt, mixing until evenly combined. The dough will become fragrant with citrus and spice.
Gradually add the flour, folding it into the wet mixture with a spatula until just combined. The dough should be soft but manageable. If it feels sticky, chill it in the fridge for 15 minutes.
In a small bowl, combine the sugar for coating with the additional cinnamon, mixing well to evenly distribute.
Scoop about 1 1/2 tablespoons of dough, roll into balls, then generously roll each in the cinnamon-sugar mixture, coating all sides evenly.
Place the coated dough balls onto the prepared baking sheet, spacing them about 5cm (2 inches) apart to allow for spreading.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden and crackly, and the tops are set with a fragrant cinnamon aroma.
Remove the cookies from the oven and let them cool on the baking sheet for 5 minutes, allowing them to set and develop their chewy, crackled texture.
Transfer the cookies to a cooling rack and let them cool completely. Once cooled, enjoy their crisp exterior, chewy center, and layered citrus-spice aroma.