Combine graham cracker crumbs and sugar in a 9-inch glass pie dish. Add melted butter and mix together. Press mixture firmly across pie dish and up sides. Set aside.
Combine milk, sugar, eggs, cornstarch, cocoa powder, and salt in a bowl and mix using an electric mixer until well combined. Pour into a saucepan and bring to a boil over medium-high heat, stirring constantly. Boil for 1 minute. Remove from heat and stir in vanilla extract.
Pour filling into crust and immediately cover with plastic wrap. Cool on counter to room temperature. Refrigerate 8 hours to overnight.