Prepare the shortbread base by combining flour, sugar, and salt in a food processor. Pulse to mix, then add cubed cold butter and pulse until mixture resembles coarse crumbs. Add egg yolk and cold water, pulsing just until dough forms clumps.
Press the dough into the bottom of a greased 9-inch springform pan, creating an even layer. Use the bottom of a measuring cup to smooth the surface. Refrigerate for 30 minutes to firm up.
Preheat your oven to 350°F (175°C) while the base is chilling. Once chilled, prick the base all over with a fork to prevent bubbling.
Blind bake the crust for 15-18 minutes until just beginning to turn golden around the edges. Remove from oven and allow to cool slightly while preparing the filling. Reduce oven temperature to 325°F (165°C).
Prepare the custard filling by heating cream, milk, and vanilla bean (if using) in a saucepan over medium heat until small bubbles form around the edges. Remove from heat, cover, and let steep for 15 minutes.
Whisk egg yolks, sugar, and salt in a large bowl until pale and slightly thickened, about 2-3 minutes. If using vanilla extract instead of bean, add it now.
Temper the egg mixture by slowly pouring about 1/4 cup of the warm cream mixture into the eggs while constantly whisking. Gradually add remaining cream, whisking continuously to prevent curdling.
Strain the custard through a fine-mesh sieve into a clean bowl to remove any bits of cooked egg and the vanilla bean pod.
Place the springform pan with pre-baked crust on a baking sheet. Carefully pour the strained custard over the crust.
Bake in the reduced-temperature oven for 35-40 minutes, or until the custard is set around the edges but still has a slight wobble in the center. It should not be completely firm.
Cool the cake completely at room temperature, then refrigerate for at least 4 hours or overnight to fully set the custard.
Just before serving, sprinkle a thin, even layer of granulated sugar over the top of the chilled custard.
Caramelize the sugar using a kitchen torch, moving constantly to avoid burning, until the sugar melts and turns a deep amber color. Let cool for 2-3 minutes until the sugar hardens before slicing.