Mix sugar, flour, and cocoa powder together in a bowl until well combined.
Mix milk, egg yolks, and vanilla together in a separate large bowl. Add flour mixture and blend custard until smooth.
Pour custard into a cast iron skillet over medium heat. Cook, stirring continually, until slightly boiling but not popping, about 5 minutes. Cook just until reasonably thickened, 3 to 5 minutes more, and remove from heat immediately. Stir hot custard to smooth out any lumps and pour into the pre-baked pie shell.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.
Combine egg whites, sugar, and vanilla for meringue in a small bowl. Beat with an electric mixer until peaks start to form. Spread meringue over custard.
Cook under the preheated broiler just until the peaks start to turn light brown, 1 to 2 minutes, being very careful not to let meringue burn.
Place the custard pie in the fridge or on Grandma's porch on a cool night until the custard congeals, about 2 hours.