Preheat the oven to 350 ℉ (175 ℃). Grease a 9-inch springform pan and line the bottom with parchment paper. Set aside.
In a small bowl, whisk together the all-purpose flour, baking powder, baking soda and salt. Then set aside the dry ingredients.
1 cup + 2 tbsp (141 g) all-purpose flour, spooned and leveled , 3/4 tsp baking powder, 1/8 tsp baking soda, 1/4 tsp salt
To a large bowl, add the sugar and lemon zest. Rub the lemon zest and sugar together with your fingertips to extract the most lemon flavor from the zest.
3/4 cup (150 g) granulated white sugar, 2 tbsp (20 g) lemon zest
Then add in the softened butter. Cream the sugar and butter together with an electric mixer on high speed until fluffy, about 1-2 minutes. (You can also use the bowl of a stand mixer fit with the paddle attachment.)
6 tbsp (84 g) unsalted butter, softened
Then add in the egg, egg yolk, and vanilla and mix on medium-high speed until smooth and pale in color, about 1-2 minutes. Scrape the sides of the bowl with a rubber spatula as needed.
1 egg, at room temperature, 1 egg yolk, at room temperature, 1 1/2 tsp vanilla
Add the flour mixture and the buttermilk to the wet ingredients a little at a time, mixing on low speed until all is combined and the batter is smooth.
1/2 cup (120 ml) buttermilk, at room temperature
Pour the batter into the prepared baking pan and spread it evenly with a mini offset spatula. Then pour the cream cheese mixture over top and spread it evenly as well.
Bake the cake for 35-40 minutes, or until the center is shiny, has a jiggle still, and the edges are a light golden brown color.
Then let the cake cool in the pan on a wire rack for 45 minutes. Then transfer the cake to the fridge to cool for 2 hours.