Prepare the Pans: Start by greasing and flouring two 8-inch round cake pans with butter, then line the bottoms with parchment paper for easy cake removal. Set aside while you gather the other ingredients.

Combine Dry Ingredients: In a mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and kosher salt until well combined.

Infuse Sugar: Place sugar, lemon zest, and dried culinary lavender in a food processor. Pulse until finely ground.

Cream Butter, Oil, and Sugar: In a stand mixer, beat the softened unsalted butter, vegetable oil, and your infused sugar mixture on medium-high speed until pale and fluffy.

Add Eggs & Vanilla: Introduce the large eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Combine Wet and Dry: Alternate adding half of the flour mixture into the butter mixture, then pour in the whole milk and fresh lemon juice. Add the remaining flour and mix just until combined.

Bake: Divide the batter evenly between the prepared cake pans. Bake in a preheated oven at 350°F for about 30-35 minutes or until a toothpick inserted comes out clean.

Cool Cakes: Let the cakes cool in the pans for 15 minutes before transferring them to a wire rack to cool completely.

Make Frosting: Beat room-temperature unsalted butter in a mixing bowl until smooth. Gradually add powdered sugar, half of the whole milk, and lemon extract, beating until light and fluffy.

Assemble the Cake: Place one cake layer on a serving plate and spread a layer of frosting on top. Place the second layer upside down.

Apply Crumb Coat: Spread a thin layer of frosting over the cake and refrigerate for 20 minutes.

Frost the Cake: Once the crumb coat is firm, frost the entire cake with a thick layer of buttercream.