For the dough: Add the flour, sugar, lemon zest and salt to a stand mixer fitted with a dough hook. Mix together for 30 seconds. Add the vanilla seeds and mix to combine. Add the butter and mix on medium speed (no higher than speed 4), until the mixture looks like coarse crumbs.
In a small bowl, beat together the egg yolks and the rum. Add to the mixer, as the machine keeps running on medium speed; the dough will start to form. As soon as it starts to leave the sides of the bowl, turn off the machine. By hand, on a flat surface, work the dough into the shape of a disk and refrigerate for about 1 hour.
Preheat the oven to 375 degrees F. Butter an 11-inch tart pan very well.
On a floured surface, roll the dough to about 1/4-inch thick and gently lay it into the tart pan. Press the dough lightly into the round edges, then, using your fingers, press on the edges of the pan, cutting off the excess. With a fork, poke the dough several times, all the way through to the pan. Brush the dough with a thin layer of egg white. Bake, with a sheet tray on the rack below it, until the edges of the dough look golden and crisp, 25 to 30 minutes.
For the filling: Whisk together the cream, sugar, yolks and eggs in a large bowl. Whisk in lemon juice and zest. Let rest while the tart shell bakes.
Remove the crust from oven, place on a sheet tray and pour the filling into the warm shell. Tap gently on the counter to release any excess air bubbles.
Lower the oven temperature to 300 degrees F.
Bake the tart in the oven for 40 minutes. The custard will appear firm with just a slight jiggle in the center of the tart. Remove from the oven and let cool for about 30 minutes.
To serve, remove the tart from the pan, sprinkle evenly with granulated sugar and use a torch to caramelize it. Repeat the final step twice to ensure a real crunch! Garnish with the powdered sugar.