Part 1: Making the Coconut Cake Layers

1. Preheat Oven and Prepare Pans: Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans. You can also line the bottoms with parchment paper rounds for extra insurance against sticking.
2. Whisk Dry Ingredients: In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt until well combined. This ensures the leavening and salt are evenly distributed throughout the dry ingredients.
3. Cream Butter and Oil: In a separate large bowl (or the bowl of a stand mixer), cream together the softened unsalted butter and vegetable oil until light and fluffy. This incorporates air into the mixture, which contributes to the cake’s texture.
4. Add Eggs and Extracts: Beat in the eggs one at a time, mixing well after each addition. Then, stir in the coconut extract and vanilla extract. Mix until just combined.
5. Alternate Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients in three additions, alternating with the buttermilk in two additions, beginning and ending with the dry ingredients. Mix on low speed until just combined after each addition. Be careful not to overmix, as this can lead to a tough cake.
6. Fold in Coconut: Gently fold in the unsweetened shredded coconut until evenly distributed throughout the batter.
7. Divide Batter and Bake: Divide the batter evenly among the prepared cake pans. Bake for 25-30 minutes, or until a wooden skewer inserted into the center of each cake layer comes out clean. The cakes should be lightly golden brown and spring back lightly when touched.
8. Cool in Pans: Let the cake layers cool in the pans for 10-15 minutes before inverting them onto a wire rack to cool completely. Cooling in the pans prevents the cakes from breaking apart while they are still warm and delicate. Ensure the cakes are completely cool before frosting and assembling.

Part 2: Making the Lemon Curd

1. Combine Ingredients in Saucepan: In a medium saucepan, whisk together the fresh lemon juice, granulated sugar, cubed unsalted butter, eggs, egg yolks, and lemon zest. Whisk until well combined.
2. Cook and Thicken: Cook over medium-low heat, stirring constantly with a whisk, until the curd thickens enough to coat the back of a spoon and reaches a temperature of 170-175°F (77-80°C). This usually takes about 8-10 minutes. It’s crucial to stir constantly to prevent the eggs from scrambling and to ensure a smooth curd. Use a candy thermometer or instant-read thermometer to monitor the temperature if you have one.
3. Strain (Optional but Recommended): Strain the lemon curd through a fine-mesh sieve into a heatproof bowl to remove any lumps or zest pieces for an ultra-smooth texture. This step is optional but will result in a perfectly silky curd.
4. Cool and Chill: Cover the surface of the lemon curd directly with plastic wrap to prevent a skin from forming. Let it cool to room temperature, then refrigerate for at least 2 hours, or until completely chilled and thickened. The curd will thicken further as it cools in the refrigerator.

Part 3: Making the Cream Cheese Frosting

1. Cream Cream Cheese and Butter: In a large bowl (or the bowl of a stand mixer), cream together the softened cream cheese and softened unsalted butter until smooth and creamy. Ensure there are no lumps of cream cheese remaining.
2. Add Extracts: Stir in the coconut extract and vanilla extract. Mix until combined.
3. Gradually Add Powdered Sugar: Gradually add the powdered sugar, one cup at a time, beating on low speed until incorporated after each addition. Once all the powdered sugar is added, increase the speed to medium and beat until the frosting is light, fluffy, and smooth. Be careful not to overbeat, as this can make the frosting too soft.

Part 4: Assembling the Cake

1. Level Cake Layers (Optional): If the cake layers are domed, use a serrated knife to carefully level the tops to create even layers. This is optional but will make stacking and frosting the cake easier.
2. Place First Layer: Place one cake layer on a serving plate or cake stand.
3. Spread Lemon Curd: Spread a generous layer of chilled lemon curd evenly over the first cake layer, leaving a small border around the edge for the frosting.
4. Top with Second Layer: Carefully place the second cake layer on top of the lemon curd.
5. Repeat Curd Layer: Spread another generous layer of lemon curd evenly over the second cake layer, again leaving a small border.
6. Top with Final Layer: Place the final cake layer on top.
7. Frost the Cake: Frost the entire cake (top and sides) with the cream cheese frosting. You can create swirls, smooth it out, or use piping techniques for a more decorative finish.
8. Garnish (Optional): If desired, garnish the cake with toasted shredded coconut, fresh lemon slices or twists, or edible flowers.
9. Chill (Optional): Refrigerate the assembled cake for at least 30 minutes to allow the frosting to set slightly before serving. This makes slicing easier and enhances the flavors.

Part 5: Serving and Enjoying

1. Slice and Serve: Slice the Coconut Cake with Lemon Curd into wedges and serve.
2. Best Served Chilled: While it can be enjoyed at room temperature, this cake is particularly delightful when slightly chilled, as the lemon curd and frosting are refreshing and the cake is wonderfully moist.
3. Enjoy! Savor the delightful combination of coconut and lemon flavors and the moist, tender texture of this incredible cake!