Preparation

1. Make the crust. Preheat the oven to 350°F with the rack in the middle position.
2. Put the cookie crumbs and melted butter into a medium mixing bowl. Using the beaters, mix on Speeds 1 to 2 to fully combine. Transfer the crumb mixture to a 9-inch pie plate. Press evenly into the bottom and sides.
3. Bake for 10 to 15 minutes, until fully set. Cool completely while preparing the filling.
4. Put the sugars, cocoa powder, cornstarch, and salt into a large, wide saucepan (be sure not to use a nonstick coated pan as the beaters could damage the coating). Using the beaters, mix on Speed 1 to combine. While still mixing on Speed 1, gradually add the half-and-half and then the eggs, and continue to mix until completely smooth.
5. Place the pan over medium-low heat. Mix occasionally on Speeds 1 to 2 to prevent the mixture from sticking to the bottom of the pan (do not leave the pan unattended).
6. Cook the mixture, continuing to mix on Speed 1, until just about boiling and thickened, and then remove from the heat. Using a heatproof spatula or spoon, stir in the chopped chocolate and butter by hand until completely incorporated. Strain the filling through a fine-mesh strainer into a medium bowl, and then transfer the filling into the cooled crust. Cover the filling directly with waxed paper or plastic wrap to prevent a skin from forming. Transfer to the refrigerator, and chill until set.
7. After the filling is set, prepare the whipped cream. Put the cream into a large mixing bowl. Using the whisk, start whipping the cream on Speed 1, gradually increasing to Speed 3, for about 1 minute so that the cream has some body. Add the sugar and continue to whip to Speed 4 until the cream forms medium-stiff peaks.
8. Top the pie evenly with the whipped cream. Garnish with chocolate curls prior to serving.