01 - Set a 9x13 inch pan filled with one inch of water on a lower oven rack. Preheat oven to 300°F. Line the bottom of a 9-inch springform pan with parchment paper.
02 - In a mixing bowl, beat cream cheese until smooth. Gradually add granulated sugar, salt, and flour, mixing on low speed until incorporated. Add lemon extract and sour cream, mixing until smooth, then blend in eggs one at a time until fully combined.
03 - Pour batter into the prepared springform pan. Place pan on the rack above the water pan and bake for 45 minutes. The cheesecake should be set around the edges but may have a slight jiggle in the center.
04 - Turn off the oven and let cheesecake rest inside for 30 minutes with the oven door slightly open. Remove and cool to room temperature. Chill in the freezer for 2–3 hours or in the refrigerator for at least 5–6 hours or overnight.
05 - Preheat oven to 350°F. Grease and flour two 9-inch round pans. In a medium bowl, whisk together cake flour, baking powder, baking soda, salt, and lemon zest. In a separate bowl, combine buttermilk, vegetable oil, lemon extract, and lemon juice.
06 - In a large bowl, beat butter at medium speed until smooth. Gradually add sugar and beat for 3–5 minutes until light and fluffy. Add eggs one at a time, mixing thoroughly after each addition.
07 - Alternately add the flour mixture and the buttermilk mixture to the butter mixture, beginning and ending with the flour. Mix just until incorporated, scraping the bowl as needed.
08 - Divide the batter evenly between the prepared pans. Bake for 20–24 minutes or until a toothpick inserted in the center comes out clean. Cool on wire racks for 10 minutes, then remove cakes from pans to cool completely.
09 - Cut butter into 1/2-inch pieces and beat until smooth. Add cream cheese and mix until fully blended. Add lemon extract and, if desired, lemon zest. Gradually add powdered sugar and mix until smooth and spreadable. If using, blend in yellow coloring gel.
10 - Place one cake layer on a serving platter and spread lightly with frosting. Release cheesecake from pan and invert onto the first cake layer. Spread a thin layer of frosting on the cheesecake, then place the second cake layer on top. Frost top and sides with remaining frosting. If the frosting becomes too soft during assembly, chill the cake for 15 minutes to firm up before serving.