Cream the sifted powdered sugar and softened butter in a stand mixer with the paddle attachment, starting on low and increasing to medium-high, until silky smooth. Add the eggs one at a time. Add the flour and salt and mix on low until just combined.

Turn the dough out, divide in half, wrap each portion in plastic wrap, and chill for at least 2 hours.

Roll one portion between two sheets of parchment at room temperature, then refrigerate until firm. Let the chilled dough become pliable, then line a 9-inch pie pan. Patch any thin or weak spots thoroughly.

Preheat the oven to 350°F convection or 375°F conventional. Line the chilled shell with crumpled parchment and fill with baking beans. Bake for about 15 minutes until the sides and bottom look matte. Remove the parchment and beans and bake for an additional 5 minutes until the bottom begins to brown. Cool completely.

Reduce the oven to 300°F conventional.

Combine the milk, cream, half the sugar, salt, and the vanilla bean seeds and pod in a saucepan. Heat to a bare simmer, remove from heat, cover, and steep at least 15 minutes (up to 45 minutes for deeper flavor). Reheat before proceeding.

Whisk the whole egg and yolks with the remaining sugar until lightened. Slowly temper the hot dairy into the eggs, whisking constantly. Whisk in vanilla extract if using. Strain through a fine mesh sieve and skim off all foam.

Set the blind-baked shell on a parchment-lined sheet pan and place it on the oven rack. Pour the warm custard directly into the shell on the rack. Bake at 300°F for 30 to 35 minutes, until the edges are set and the center jiggles as one cohesive mass. Shield the crust edges if browning.

Cool to room temperature, then chill for at least 5 hours, ideally overnight.

At service: slice the pie and place individual slices on a large plate. Sprinkle an even layer of granulated sugar over each slice and torch to a deep caramel immediately before serving.