Preheat oven to 350°F.
Roll out pie crust on a lightly floured work surface and fit into a 9-inch pie pan. Trim edges.
In a large bowl, whisk together sugar and cocoa. Add melted butter, evaporated milk, eggs, and vanilla extract. Whisk to combine.
Pour into pie shell, and place on a baking sheet to catch any overflow.
Bake about 45 minutes; the center will still be jiggly.
Cool to room temperature before serving.