Preheat your oven to 350°F. Grease and line an 8-inch square baking pan with unbleached parchment paper or nonstick aluminum foil that overhangs the sides of the pan, and set it aside.
In a double boiler or a medium-sized microwave safe bowl, melt the chocolate and until melted and smooth. In the microwave, melt in 30-second increments at 70% power, stirring in between. Set the melted chocolate aside to cool briefly.
In a separate, large bowl, place the butter and sugar and beat with a handheld mixer on medium-high speed until becoming creamy (about 3 minutes). Add the eggs one at a time, beating very well after each addition.
Add the vanilla and salt, and beat on high speed until light and fluffy (about 1 minute).
Add the cocoa powder and mix by hand, then beat on low speed until the cocoa powder is absorbed.
Add the melted and cooled chocolate and mix well until smooth and glossy (2 to 3 minutes).
Pour the mixture into the prepared baking pan, spread it into an even layer and tap the pan on a flat surface to break any large air bubbles.
Sprinkle the top evenly with the (optional) chocolate chips and press the chips into the batter to help them adhere.
Place the pan in the center of the preheated oven and bake until the brownies are puffed in the center and the center doesn’t jiggle when shaken gently from side to side (22 to 25 minutes). Do not overbake.
Remove the pan from the oven, and place it on a wire rack to cool completely, still in the pan.
Once the brownies are nearly cool, place the pan in the refrigerator to chill until firm to the touch (about 1 hour). This will make slicing much easier.
Remove the brownies from the pan by lifting up on the foil. Use a large, sharp knife to slice into 9 equal squares.
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Notes
Dairy free—Try using vegan butter, virgin coconut oil (the kind that's soft solid at room temperature), or butter-flavored Spectrum or Crisco shortening.