Preheat the oven to 350 degrees.
Grease a 9-by-9-inch square baking pan (you can also line the pan with aluminum foil and grease the foil).**
Melt the butter and chocolates in a medium to large saucepan over low heat, or use a microwave. Watch carefully. Meanwhile, gently beat the eggs in a bowl and stir in the vanilla.
When the butter and chocolate mixture is melted, take it off the heat and stir in the sugar, eggs, and vanilla. Add the flour and cocoa powder and stir well with a spoon or whisk, but do not overmix.
Pour the brownie batter into the prepared pan. (If you’re using chocolate chips or nuts, mix them into the batter first or sprinkle them on top of the batter before baking, pressing them down a bit into the batter.) Bake for 30-35 minutes, or until a knife or toothpick inserted in the center comes out almost clean. Let the brownies cool before lifting them from the pan.
