Preheat your oven to 350°F (175°C) and prepare a baking dish.
Melt the butter in a medium saucepan over low heat and whisk in the sugar until combined.
Remove the saucepan from heat and let it slightly cool before whisking in the eggs and vanilla extract.
In a separate bowl, sift together the flour, cocoa powder, and salt.
Gradually fold the dry ingredients into the wet mixture until just combined.
Add the chocolate chips and nuts (if using), folding gently to distribute them evenly.
Pour the brownie batter into the prepared baking dish and spread it evenly.
Bake in the preheated oven for 25 to 30 minutes, until the tops are set and a toothpick comes out with a few moist crumbs.
Allow the brownies to cool in the pan before cutting into squares and serving.