Preheat the oven to 350°F convection or 375°F conventional. If making a homemade crust, roll one portion of pie dough on a lightly floured surface to about ⅛-inch thick, then chill flat on a baking sheet for 30 minutes to relax the gluten and re-solidify the butter.

Drape the chilled dough over a 9-inch pie dish. Allow it to warm just enough to be workable, then lift the edges and let it settle onto the bottom. Press the sides gently to fit, leaving the edges to overhang, then roll the overhang under and press it against the rim to seal. Flute by pressing one knuckle from the outside against two from the inside. Chill the shaped crust for 10 to 30 minutes.

Crumple a sheet of parchment paper, smooth it out, and press it into the chilled crust. Fill with pie weights, dried beans, or rice. Blind bake for 15 to 20 minutes, until the crust has just started to color and no longer looks raw, then remove the weights and parchment.

Reduce oven temperature to 325°F convection or 350°F conventional. Set a large heatproof bowl over a pot with about an inch of simmering water, making sure the bottom of the bowl does not touch the water. Add the butter, chopped dark chocolate, cocoa powder, espresso powder, and kosher salt. Stir occasionally until fully melted, then remove from the heat. The mixture should be melted and smooth but not steaming hot.

In a separate bowl, whisk the whole eggs and egg yolks together until slightly lightened and no visible whites remain. Whisk in the granulated sugar and brown sugar until the mixture is pale and fluffy.

Pour the chocolate mixture into the egg mixture all at once and whisk immediately and thoroughly. Work quickly so the chocolate does not seize and the eggs do not scramble from the residual heat.

Pour the filling into the par-baked crust and transfer to the preheated oven. Bake for 40 minutes, or until the filling puffs slightly in the center and jiggles as one cohesive unit when you nudge the rack, like Jell-O or a set cheesecake. Do not pierce the filling to test for doneness.

Cool completely at room temperature before wrapping and refrigerating. Slice cold with a sharp knife dipped in hot water, wiping the blade between each cut.