Preheat your oven to 350°F (175°C). Grease an 8×8 inch baking pan or line it with parchment paper for easy removal after baking.
Melt the butter in a medium saucepan over low heat. Once melted, remove it from heat and let it cool slightly before mixing with other ingredients.
In a large bowl, mix together the melted butter, granulated sugar, and brown sugar until creamy and well combined. Beat in the eggs one at a time, followed by stirring in the vanilla extract for added flavor.
In another bowl, sift together the flour, cocoa powder, and salt. Gradually add this dry mixture to the wet ingredients until just blended; be careful not to overmix as this can lead to tough brownies.
Pour the batter into the prepared pan and spread it evenly. Bake for 20-25 minutes until a toothpick inserted comes out with moist crumbs, which indicates they are perfectly fudgy.