Preheat your oven to 350°F and line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the egg and vanilla extract, mixing until fully incorporated.
In a separate bowl, whisk together the flour, baking powder, baking soda, cream of tartar, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until a soft dough forms.
Scoop the dough into 12 evenly sized balls and place them on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are set and slightly golden.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely while you make your buttercream filling.