Step 1

Cream sugar and yolks together in a large saucepan. Add milk, cocoa powder, cornstarch, and salt; whisk until no lumps remain. Add half-and-half and heat over medium heat, whisking constantly until filling is thickened, about 20 minutes.

Step 2

Turn off heat when filling starts to bubble; continue to stir for 1 minute. Remove thickened filling from the warm burner. Add butter and vanilla extract, stirring well until melted and well incorporated. Let filling sit to cool slightly, about 10 minutes.

Step 3

Stir filling well and pour into graham cracker crust, smoothing the top with a spatula. Chill, uncovered, in the refrigerator for 4 hours.