Preheat oven to 350F. Grease two 8″ cake pans with butter, add a piece parchment paper, cut to size to the bottom of the pan, then grease the parchment paper and dust lightly with flour, shaking out any excess (this helps avoid any sticking).

In the bowl of a stand mixer, cream softened butter, sugar and oil together until light and fluffy, about 5 minutes. Add the eggs one at a time, mixing after each addition to combine. Add in the lemon zest and vanilla extract and mix.

In a measuring cup, mix the lemon juice and milk, let sit for 5 minutes. In a separate bowl, sift together the flour, baking powder, baking soda and salt. Starting with the flour, alternate adding the flour mixture and the lemon/milk mixture to the stand mixer, mixing after each addition until just combined.

Divide between two 8 inch pans and bake for 30 minutes, or until a cake tester inserted in the center comes out clean.  If making into cupcakes, bake for 17-19 minutes. Remove from oven and let cool on a rack for 5 minutes before removing from pans. Allow to cool completely before decorating, at least one hour.

To assemble cake, level the cakes with a large serrated knife. Pipe a thick circle of buttercream around the edge of bottom layer of cake, then place in the fridge for it to harden, about 15 minutes. Remove from fridge and add lemon curd inside the buttercream barrier. Add the top layer of cake and frost a crumb coat over the cake. This is a very thin layer of buttercream, which you then refrigerate to harden. This prevent your final coating of buttercream from having any crumbs in it.  After the crumb coat has hardened add your final layer of buttercream using an offset spatula.

In a large sauce pan, combine sugar and cornstarch, whisk together to combine. Add in the egg yolks and 1 cup of milk and whisk until smooth.  Once smooth, add in remaining milk and vanilla extract.  Cook over medium heat, whisking constantly until thickened, this will take several minutes.

Once mixture is nice and thick, remove from heat and pour through a sieve onto a large plate. Place saran wrap directly onto the surface of the pudding and allow to cool to room temperature.

When mixture is cool, begin by beating the butter in a stand mixer, or with a hand mixer, until it gets fluffy and light in colour.  Add the pudding to the butter 1 tbsp at a time, and mix until fully combined before adding another tbsp.  Continue until all pudding is added. To remove air bubbles for pipping, smoosh the pudding with a spatula for a minute or so.

Buttercream can be stored in the fridge for 4 days, or in the freezer for 1 month. Allow to defrost in the fridge overnight, then bring to room temperature before beating again to smooth out.