Preheat the oven to 350˚F (180˚C). Line a 10-inch (25-cm) cast iron pan with parchment paper.
2. Step
In a large bowl, mix the butter with 1 teaspoon of vanilla extract until light and fluffy.
3. Step
Add the granulated sugar, then the brown sugar, and mix until well incorporated.
4. Step
Add the egg and stir until thoroughly incorporated.
5. Step
Using a fine mesh sieve, sift the flour, cream of tartar, baking soda, and salt into the dough. Combine with a spatula until evenly mixed.
6. Step
Spread the cookie dough in an even layer in the prepared pan. Chill in the fridge for 30 minutes, then bake for 15-18 minutes until lightly golden. Let cool.
7. Step
In a medium bowl, combine the cream cheese, powdered sugar, and remaining ½ teaspoon of vanilla extract until well incorporated.
8. Step
Spread half of the frosting onto a quarter of the cooled cookie and the other half on the diagonally opposite corner.
9. Step
Frost the other quarters with the chocolate hazelnut spread.