Preheat the oven to 350F/177C and line two, 8-inch cake pans with parchment paper, leaving the sides ungreased. Prepare the liquid ingredients first: in a large mixing bowl, combine the oil, milk, eggs, sugar and vanilla. Using a hand mixer, stand mixer or whisk, beat the ingredients together for 2 to 3 minutes on high speed until the eggs are well beaten. In a separate bowl, combine the dry ingredients: flour, baking powder and soda, and salt. Sift the dry ingredients into the cake batter and mix on medium speed for 1 minute, just until the flour is incorporated. Watch my video recipe to see how it's done.
Zest 2 to 3 lemons and add the zest into the prepared cake batter. In a small bowl, toss together the raspberries and cornstarch, making sure the berries are well coated. Use a spatula to gently fold in the berries and zest. Divide the cake batter evenly between the two pans using a large spoon. Bake the cake layers in the preheated oven for 32 to 35 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake layers to cool in the pans for about 20 minutes, then cool completely on a wire rack.
While the cake is baking, prepare the lemon curd. The curd needs to be completely cooled before using! *If you don't have time to make this lemon curd, use store-bought, premade curd instead.* I recommend juicing fresh lemons for the recipe. Double strain the juice for smoothest lemon curd. Set juice aside. In a medium sized stainless steel pot, combine the eggs, egg yolks and sugar. Whisk vigorously for 3 to 4 minutes, until the mixture is thick and pale in color; it should ribbon off the whisk. Pour in the lemon juice; whisk to combine.
Cook the lemon curd over medium-low heat, stirring constantly along the bottom of the pan. Cook for 4 to 5 minutes, until the curd thickens and starts to bubble lightly. Remove from heat immediately. Add the unsalted butter and vanilla and whisk until the butter is completely melted. Transfer the curd into a glass bowl or glass jar and cover with plastic wrap to prevent a film from forming over the top. Allow the lemon filling to cool slightly, then place into the refrigerator to cool completely.
Once the cake layers are cooled, prepare the cream cheese frosting. If you are making the frosting ahead of time, keep it refrigerated until ready to use. Soften the cream cheese and butter at room temperature until slightly soft to touch - not melted or too soft! Place the butter into a stand mixer bowl and use a whisk attachment to whisk the butter. Whisk on high speed for about 5 minutes, scraping down the sides of the mixing bowl often to get all the butter creamed. Add the softened cream cheese next and whisk again for 2 to 3 minutes, scraping down the sides of the mixing bowl often, until the mixture is uniform and smooth.
Add the vanilla, salt and confectioner's sugar. Whisk on low speed first until the sugar is incorporated, then turn the speed up and whisk on high for 2 to 3 minutes, until the frosting is light and fluffy. Add in the lemon zest last and whisk again for 30 seconds. If desired, you can also add 1 tsp lemon oil, 1 tablespoon of lemon juice or 1 tsp citric acid for more lemon flavor.
To assemble the cake, first level the cooled cake layers using a long serrated knife; if needed. Spread a generous amount of the lemon frosting onto the first cake layer. Spread it evenly, then add a few tablespoons of lemon curd in the center, spreading it within 1/2-inch of the edge of the cake. Top with the second cake layer and frost the top and sides of the cake, smoothing down with cake spatulas. Apply a crumb coat of frosting, then refrigerate the cake for 15 to 20 minutes before applying the final coat of frosting. Watch my video recipe to see how it's done.
Garnish the top of the cake with more lemon curd and fresh raspberries. If not serving within a few hours, keep the cake in the refrigerator. The cake can be made ahead of time and will store well in the refrigerator for up to 4 or 5 days, if well covered. When ready to enjoy, remove the cake from the fridge and let it stand at room temperature for 1 hour to soften.