Preheat oven to 325 degrees F. Line the bottom and sides of an 8-inch square baking pan with parchment paper and set aside.
Add enough water to a medium saucepan so that it is 1 to 2 inches deep. Heat water until barely simmering.
Combine butter, sugar, cocoa powder, and salt in a medium heat-safe bowl. Rest the bowl over simmering water. Stir the mixture occasionally until the butter has melted and the mixture is quite warm.
Remove the bowl from heat and set aside for 3 to 5 minutes until it is only warm, not hot. Stir in the vanilla with a spoon. Then add the eggs, one at a time, stirring vigorously after each one.
Then add the flour and stir until fully incorporated, then beat with the wooden spoon until well combined.
Bake the brownies for 20 to 25 minutes or until a toothpick can be inserted into the center and come out with a few moist crumbs.
Cool completely. Serve and enjoy!