Preheat oven to 300 degrees F (150 degrees C). Lightly grease an 8-inch pie plate.

Sift together flour, cocoa powder, and salt in a medium bowl; set aside.

Stir together sugar and eggs in a large bowl until smooth. Add flour mixture; stir just until combined. Pour in melted butter and vanilla; stir until well combined. Pour into the prepared pie plate.

Bake on the lower rack of the preheated oven until the center has slightly set, about 35 minutes. Allow cake to cool for 1 hour in the pie plate. Serve warm or refrigerate overnight and serve cold.