Slide a metal mixing bowl and beaters into the freezer for 10 minutes. Finely chop the dark chocolate and set aside. Lightly butter a 9-inch pie plate. Preheat the oven to 350°F (177°C).
Make the crust: Stir graham crumbs with brown sugar, then drizzle in melted butter and mix until the texture resembles damp sand. Firmly press into the bottom and up the sides of the pie plate. Bake 10–12 minutes until fragrant and a shade deeper in color. Cool 20 minutes, then refrigerate 10 minutes to help it set.
Start the pudding base: In a medium saucepan off heat, whisk together sugar, cornstarch, cocoa powder, espresso powder, and salt. Gradually whisk in the milk until smooth, then whisk in the egg yolks until fully combined.
Cook the pudding: Set the pan over medium heat and cook, whisking often and scraping the corners with a flexible spatula, until thick bubbles break the surface and the mixture coats the spatula, 8–10 minutes. Reduce heat to low and cook 1 minute more while stirring to remove any starchy taste.
Finish off heat: Remove from the burner, add the chopped chocolate, cover the pan for 2 minutes to melt, then whisk until glossy and smooth. Stir in the vanilla.
Strain and cool briefly: Push the pudding through a fine-mesh sieve into a clean bowl. Set the bowl over an ice bath and stir 3–5 minutes until the pudding is warm (not hot) to the touch.
Assemble: Pour the warm pudding into the cooled crust and smooth the top. Press plastic wrap directly onto the surface, leaving a small gap at one edge for steam to escape. Refrigerate until fully set, at least 4 hours or up to 24 hours.
Whipped cream: In the chilled bowl, beat the cold heavy cream with powdered sugar and vanilla to medium-stiff peaks, 2–3 minutes with a hand mixer. Swirl the cream over the cold pie.
Slice and serve: Warm a knife under hot water, wipe dry, and cut clean slices. Return leftovers to the refrigerator promptly.