Melt butter in saucepan with cocoa and stir until smooth. Remove from heat and allow to cool for a few minutes, then transfer to a large bowl. Whisk in eggs, one at a time. Stir in vanilla.
In a separate bowl, combine sugar, flour, nuts and salt. Add to the cocoa-butter mixture. Stir until just combined.
Pour into a greased 8 x 8-inch-square pan. Bake 30 to 35 minutes. Do not overbake; the brownies should be gooey. Let cool, then cut into bars.