Prepare the shortbread. Place flour, powdered sugar, vanilla, butter, and salt in a food processor. Pulse several times until mixed well. Transfer ingredients into large bowl, creating a well in the center for your eggs.
Using a fork (or your hands!) begin incorporating eggs into your flour mixture. Once everything has formed into a shaggy mass, transfer the dough onto a floured work surface and knead well. The dough should be smooth! Split the dough into two disks: one with 2/3 of the dough and the other with 1/3. Wrap well in plastic wrap and allow dough to rest in the refrigerator while you prepare your pastry cream.
To prepare the pastry cream, place a large pot on the stove with milk, take the vanilla bean and carefully, with the back end of a knife, extract the seeds by scraping. Add the seeds and the vanilla pod to the milk and on low heat, bring the milk to a low simmer. As soon as the milk begins simmering, remove from heat to allow the milk to infuse with the vanilla bean. This should only take about 5 to 7 minutes max.
Meanwhile, in a large bowl and with an electric mixer, beat your egg yolks and sugar until pale yellow and smooth and slightly fluffy. Gradually add sifted flour and lemon zest.
Remove the vanilla pod from the milk and add the mixture with eggs. Do this little by little while constantly whisking your egg mixture so as not to scramble your eggs! Return the entire mixture to the stove on low heat, whisking constantly to thicken the mixture. This will happen all at once, so be on watch! When the cream is very thick, turn off the heat and, using a spatula, empty into a low, wide bowl. Allow it to cool for 30 minutes, then cover it so the surface is in contact with plastic wrap, so that it does not create a skin. Transfer to a refrigerator. This can be kept in a refrigerator for up to 3 days and can be frozen for up to 2 months.
Remove the dough from the fridge, allow it to come to room temperature. Taking the larger disk of dough, roll it out into a circle that will cover a 9-inch pan. For this, I use a tart pan with a bottom that's easily removed. Springform pans work well too! Butter and flour the pan. Make sure that the dough is large enough to line the pan (covering the sides generously). Wrap the dough onto your rolling pin and unroll it onto the cake pan, pressing it gently down into the pan and being sure to cover the pan's bottom and sides.
Remove the excess pastry using a sharp paring knife. With a fork, dock the surface of the dough and pour in the pastry cream, using a spatula to make a slight mound in the center (this will help it from collapsing after baking). Roll out your remaining pastry in a disk just a bit larger than your pan. Again, transfer the dough by wrapping onto your rolling pin and unroll over your dreamy cream mountain.
Create a nice seal on the cake by pinching the edges of the crust closed. You can decorate these as you'd like—and be sure to dock the top crust with a fork. Brush the entire surface of the crust with an egg wash (egg and water, or egg and milk if you prefer). Sprinkle generously with pinoli and bake at 356° F (180° C) for 45 to 50 minutes.
Allow the cake to cool before serving. Finish with a generous dusting of powdered sugar, like any good Italian dessert. You can also refrigerate this completely; it's just as delicious.