Mix sugar, flour, and cocoa powder together in a bowl until well combined.

Mix milk, egg yolks, and vanilla extract 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.

Beat egg whites, sugar, and vanilla extract together in a small bowl until peaks start to form. Spread the thick meringue mixture on top of the 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 the 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.