Bring the whole milk to a simmer over low-medium heat in a medium-sized pot.
In a bowl, whisk together the egg yolks and sugar. Add the cornstarch and whisk until lump-free.
Whisking continually, pour 1/2 cup of the hot milk into the egg mixture.
Return the pot of milk to the stove and, whisking vigorously, pour the egg mixture into the pot.
Add the vanilla extract and continue cooking over low-medium heat until the filling thickens to a pudding-like consistency (about 2-3 minutes).
Pour into a bowl, cover with a piece of plastic wrap pressed against the surface of the filling, and refrigerate.
Cake:
In the bowl of a stand mixer, cream the butter and sugar on medium-high until light and fluffy (about 2-3 minutes).
With the mixer on low, add the egg yolks one at a time, mixing until just combined.
Combine the remaining dry ingredients (flour and baking powder) in one bowl and the remaining wet ingredients (milk and vanilla extract) in another.
With the mixer still on low, add the dry ingredients in two parts, alternating with the wet ingredients in one part. Mix until just combined.
Grease a 15" x 10" jelly roll/cookie pan and cover with parchment paper (the grease is so the parchment paper sticks).
Spread the batter out onto the parchment paper-lined pan, working it all the way to the edges. The batter will be thick so this may take some work.
In a clean bowl, whip the egg whites and sugar for the meringue on high until stiff, glossy peaks form (about 5-10 minutes depending on the power of your mixer).
Spread the meringue evenly over the cake batter and top with sliced almonds.
Bake at 325F for 30-35 minutes, or until the meringue is a light golden brown.
Remove from the oven and allow to cool completely in its pan.
Assembly:
In a medium-large bowl, whip the heavy whipping cream for the filling until it holds stiff peaks.
Fold the whipped cream into the cooled bowl of filling from the fridge.
Using a serrated knife and a gentle sawing motion, cut the cake in half.
Place one half, meringue side down, onto a plate.
Cover with the filling working it all the way out to the edges.
Place the other cake half, meringue side up, on top of the filling and apply gentle pressure to seal them together.
Place the cake in the refrigerator and allow to set for one hour before serving.
Notes
Start with a perfectly clean bowl for meringues: This may seem like a no-brainer but even a little bit of grease can ruin your meringue. Whatever you use, make sure it’s been thoroughly scrubbed with warm, soapy water.
Don’t use plastic bowls to make meringue: To the point above, it’s very hard to completely remove fats from plastic bowls and kitchen utensils, which tend to develop a greasy coating over time. Instead, use a glass, metal, or ceramic bowl.
Crack your eggs into a separate bowl: Egg yolks = fat and as we’ve established, fats will keep your meringue from reaching its full potential. To avoid having a single yolk ruin the whole batch, be sure to crack and separate your eggs over a small bowl before adding the white to the rest of the batch.
Cooling the vaniljekrem faster: You can speed up the cooling process by placing the bowl of cooked cream over an ice bath. Stir continually to keep it from clumping as it cools.
Storage: This cake can be stored in the refrigerator for up to 3-4 days.