Make the tart shell: Heat your oven to 350°F. In a food processor: Combine the flour, salt, and sugar in the bowl of a food processor. Add butter and vanilla to the bowl, then run the machine until the mixture forms large clumps — just keep running it; it might take another 30 seconds for it to come together, but it will. Transfer dough to a 10-inch round or 9-inch square tart pan with a removable bottom set and press the dough evenly across the bottom and up the sides. Transfer to freezer for 15 minutes, until solid.
Parbake crust: Once firm, prick all over with a fork. Coat a piece of foil with nonstick spray, and press it oiled-side-down tightly against the frozen crust, so it is fully molded to the shape. Bake tart with foil (no pie weights needed) for 20 minutes, then carefully, gently, a little at a time, peel back foil and discard. Return to oven for 10 to 20 minutes (keep an eye on it, I overbaked mine!), until lightly browned all over. Let cool to room temperature, ideally, but it’s okay to use if it’s still lukewarm.
Meanwhile, make the filling: Remove the zest of 4 limes with a vegetable peeler or zester/rasp, being careful to avoid the white pith. Squeeze the limes to make 1/2 cup of juice and set the juice aside. Put the zest in a food processor fitted with a steel blade. Add the sugar and salt and process for 2 to 3 minutes, until the zest is very finely minced. Add butter and blend until fully disperse into the sugar. Add eggs, two at a time, and blend to combine. Add lime juice and blend for a second or two.
Transfer the filling to a medium saucepan and cook over low heat, stirring constantly, until thickened, about 5 to 10 minutes. The lime curd will thicken at about 175°F, or just below a simmer. Remove from heat and pour into the tart shell. Transfer to the fridge to cool and set.
To serve: Add dolloped of lightly sweetened whipped cream (if you wish) and serve cool, in wedges or squares.