Score down the length of the vanilla bean, if using, and remove the seeds by scraping a knife down the inside of each half (keep the pod for making vanilla sugar).
Cream together the butter, powdered sugar, and salt and then rub in the flour, vanilla seeds, lemon zest, and egg yolks — you can do all this by hand or in a food processor. When the mixture looks like coarse breadcrumbs, add the cold milk or water. Pat and gently work the mixture together until you have a ball of dough, then flour it lightly and roll it into a large sausage shape — don't work the pastry too much, otherwise it will become too elastic and chewy, not flaky and short as you want it to be.
Wrap the dough in plastic wrap and place in the fridge to rest for at least an hour. Remove it from the fridge, slice it up, and line an 11-inch tart mold with the slivers. Push them together, then tidy up the sides by trimming off any excess. Place the tart mold in the freezer for an hour.
Preheat the oven to 350°F (175°C), then take the pastry out of the freezer and bake for around 15 minutes or until lightly golden. Remove from the oven, place to one side, and turn the heat down to 325°F (160°C).
Make the frangipane:
Blitz the whole almonds in a food processor until you have a fine powder and put this into a bowl.
Now blitz the butter and sugar until light and creamy. Add this to the almonds with the lightly beaten eggs and fold in until completely mixed and smooth. Place in the fridge to firm up slightly.
Smear the jam over the bottom of the pastry shell, pour the chilled frangipane mixture on top, and sprinkle with some sliced blanched almonds. Bake the tart for about 40 minutes, or until the almond mixture has become firm and golden on the outside but is still soft in the middle.
Allow to cool for about 30 minutes and serve with crème fraîche or custard.