Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan and set aside.
In a medium-sized saucepan, melt the butter over low heat. Once melted, remove the pan from heat and stir in the sugar until well combined.
Add the eggs one at a time, stirring well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and salt. Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Pour the batter into the prepared baking pan, spreading it evenly with a spatula.
Bake the brownies for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the brownies to cool completely before slicing and serving.