Preheat your oven to 300°F (150°C) and line the bottom of a springform pan with parchment paper. In a large mixing bowl, blend softened cream cheese with granulated sugar, salt, flour, sour cream, and lemon extract until smooth. Gradually incorporate eggs one at a time, mixing well after each addition. Pour the cheesecake batter into the prepared pan; bake for 45 minutes, until the edges are set but the center slightly wobbles. Cool in the oven to prevent cracking.

Once the cheesecake layer is baked, turn off the oven and leave the door ajar to let the cheesecake cool gradually. After about an hour, transfer it to the fridge for at least 4 hours, or overnight if possible, until fully chilled and set.

While the cheesecake chills, preheat your oven to 350°F (175°C) and grease two round 9-inch cake pans. In a medium bowl, whisk together the cake flour, baking powder, and baking soda.

In a separate bowl, cream together butter and sugar until light and fluffy. Beat in eggs, adding the dry ingredients alternately with buttermilk and vegetable oil until just combined. Pour the batter evenly into the prepared pans and bake for 20-24 minutes, or until a toothpick comes out clean. Allow them to cool completely.

In a mixing bowl, beat together softened butter and cream cheese with an electric mixer until creamy and well-combined. Gradually add powdered sugar and lemon extract, adjusting to your desired sweetness and consistency. Mix until smooth; you want the frosting to be thick but spreadable.

Once the lemon cake layers are cooled, place the first layer on a serving plate. Generously spread a layer of lemon cream cheese frosting over the top, then carefully invert the chilled cheesecake layer on top of the frosting. Next, add the second lemon cake layer on top of the cheesecake. Frost the top and sides with the remaining lemon cream cheese frosting, smoothing it out for a beautiful finish.