Preheat oven to 350F.
Grease an 8-inch square pan.
In a medium bowl, mix the butter and the sugar. Add the vanilla, and salt and beat well with a wooden spoon.
Add in the eggs, one at a time, beating well between each addition. Beat well, about 60 strokes.
Stir in the flour and cocoa powder, mix just until flour and cocoa is blended through.
Pour batter into prepared pan and bake for 20 minutes, or until brownies are just beginning to pull away from the sides of the pan. A toothpick inserted into the centre will still be fudgy.
Let cool, then cut into 16 pieces.
Serve with a glass of cold milk or a scoop of ice cream.