Preheat the oven to 350° F. Grease and line an 8X8-inch baking pan with parchment, set aside.
In a medium-sized bowl, whisk together the slightly cooled melted butter and granulated sugar. Whisk well for 1-2 minutes. Add the eggs and vanilla extract, whisk for an additional 2-3 minutes until light in color.
In a small bowl, whisk together the flour, cocoa powder, and salt. Carefully fold the dry ingredients into the egg mixture, until well incorporated. Fold in ⅓ cup of the semi-sweet chocolate chips.
Pour the batter into the prepared pan, spread out evenly. Bake for about 20 minutes, or until set.
Immediately after pulling out the baked brownies, sprinkle the top with marshmallows, walnuts, and the remaining ⅓ cup of chocolate chips. Bake for an additional 2 minutes, or until marshmallows have softened and the chocolate chips are gooey.
Allow the brownies to cool for at least 1 hour before serving. Serve room temperature or warm.
Store the brownies in an airtight container, layers separated by wax paper, for up to 3 days at room temperature and up to 5 days in the refrigerator. To reheat: microwave one brownie for 15 - 20 seconds.