Preheat oven to 325 degrees. Line an 8x8-inch square baking dish with parchment paper, leaving a 1-inch overhang, or grease well and coat with flour. Set aside.
Melt butter in a large microwave-safe bowl or measuring cup. (Alternatively, melt butter in a large saucepan on the stove, then turn off heat and proceed.) Add cocoa powder and stir with a wooden spoon until smooth. Stir in sugar, salt, eggs and vanilla extract. Add flour and stir until well combined.
Spread batter evenly into the prepared pan - you'll need to work at it, spreading it out with the back of a wooden spoon - the batter is very stiff. Bake for about 30 minutes, until edges are set and centre is firm but still just slightly underdone. A toothpick should come out with a few moist crumbs attached. Let cool 10 minutes at least before lifting out by parchment overhang to slice into squares.