Preheat the oven to 350 degrees F (175 degrees C).

Melt butter in a cast iron skillet over medium-low heat.

Combine 1 cup sugar with cocoa and flour. Beat egg yolks with milk and add to the sugar mixture.

Add sugar and egg mixture to the skillet with melted butter and cook gently, stirring constantly until thick. (Watch this mixture closely as it has a tendency to burn.) Add vanilla. Pour the mixture into the baked crust.

Beat egg whites until soft peaks form; add remaining 1/4 cup sugar and beat until meringue is glossy and stiff peaks form. Spread beaten egg whites over the hot filling. Be sure whites touch the edges of the crust.

Bake in the preheated oven until the meringue is golden brown, 10 to 15 minutes.