In a saucepan, combine sugar, cocoa powder, cornstarch, and salt. Gradually whisk in milk until smooth. Cook over medium heat, stirring constantly, until mixture thickens and comes to a boil. Boil for 1 minute, then remove from heat.
Stir in instant coffee granules and vanilla extract until well blended. Pour mixture into pre-made pie crust. Chill in the refrigerator for at least 2 hours or until set.