Butter an 8 inch cake pan and line the bottom with parchment paper. Preheat oven to 350° F.
In the bowl of a stand mixer, whisk together flour, fir tip sugar, sugar, baking powder, baking soda, and salt.
Add soft butter and lemon zest, mixing until butter breaks down into small pieces.
Add eggs and buttermilk. Mix on medium until well combined and fluffy, 1-3 minutes.
Pour cake batter into prepared pan and bake until cake springs back when touched, about 25-35 minutes. Allow to cool completely, then invert from pan and remove parchment paper.