Preheat oven to 300°F (150 degrees C). Prepare an 8-inch pie plate.
Sift together the flour, cocoa powder, and salt then set aside.
Whisk the eggs into the sugar until smooth. (About three minutes on medium speed in a stand mixer or a hand-held mixer on high)
Add the flour mixture, and stir by hand just until combined.
Pour in the vanilla extract and melted butter; stir until well combined.
Pour into prepared pie plate.
Bake on the lower rack of oven for 35 minutes, or until the center has slightly set.
Allow the cake to cool for several minutes in the pan before serving.
Optional: Sprinkle with confectioners' sugar or add fresh berries for color.