Preheat oven to 300 degrees F (150 degrees C). Lightly grease an 8-inch pie plate.
Sift together the flour, cocoa powder, and salt; set aside. Stir the eggs into the sugar until smooth. Add the flour mixture, and stir just until combined. Pour in the vanilla extract and butter; stir until well combined. Pour into prepared pie plate.
Bake on the lower rack of the preheated oven for 35 minutes, or until the center has slightly set. Allow cake to cool for 1 hour in the pie plate. Serve warm, or refrigerate overnight and serve cold.