Preheat your oven to 300°F and place a pan of water on a lower rack for humidity. In a mixing bowl, beat the softened cream cheese until smooth and creamy. Gradually add sugar, salt, and flour, mixing until fully combined. Incorporate sour cream and lemon extract, then slowly add eggs one at a time, ensuring the mixture remains smooth. Pour the batter into a prepared springform pan and bake for 45 minutes, or until the center is slightly jiggly. Allow it to cool gradually in the oven to prevent cracks, then refrigerate.

While the cheesecake is cooling, preheat your oven to 350°F and grease two 9-inch round cake pans. In a large bowl, whisk together the cake flour, baking powder, baking soda, salt, and lemon zest. In a separate bowl, combine buttermilk, butter, lemon extract, and lemon juice. Cream softened butter with granulated sugar until light and fluffy, then mix in eggs one at a time. Gradually alternate adding the dry and wet mixtures to the batter, being careful not to overmix. Pour the batter into the prepared pans and bake for 20-24 minutes, or until a toothpick inserted into the center comes out clean. Let the layers cool for 10 minutes before transferring them to wire racks.

In a large mixing bowl, beat the softened butter until creamy and smooth. Add the cream cheese and lemon extract, mixing until well combined. Gradually add the powdered sugar, beating on low speed initially to avoid a sugar cloud, then increase to medium speed until the frosting becomes light and fluffy.

Begin assembling your Creamy Lemon Cheesecake Cake by placing one cake layer on a serving plate. Generously spread a layer of frosting on top, then carefully invert the chilled cheesecake onto the frosted layer. Spread a layer of frosting over the cheesecake, then gently place the second cake layer on top. Finally, frost the sides and top of the assembled cake for a smooth finish. Chill the cake if necessary before serving.