Preheat & Prep. To start, preheat the oven to 350 degrees F. Line a metal 8x8 pan with parchment paper and set aside.
Melt Chocolate & Butter. In a microwave safe bowl, combine 1 1/3 cups chocolate chips with the butter and melt in 15-20 second intervals until smooth. (If you have a low power setting, I recommend it here to avoid scorching the chocolate.) Let chocolate cool slightly while you work on the eggs and sugar.
Whip Sugar & Eggs. In a large bowl (glass works best!), combine granulated sugar and eggs. Whip with a whisk or handheld electric mixer for 2-3 minutes, or until doubled in volume, much lighter in color, and the sugar is almost completely dissolved. Do NOT rush this step!
Combine Wet Ingredients. Add chocolate mixture to the egg mixture along with the vanilla and mix until smooth and evenly blended.
Add Dry Ingredients. Next, add gluten-free flour, cocoa powder, and salt and mix until just combined and no dry patches remain.
Bake & Cool Brownies. Smooth batter into the prepared pan and bake 18-20 minutes, or until the top is set and glossy and a toothpick inserted in the center comes out clean with just a few moist crumbs. (It shouldn't be full of wet batter.) Let the brownies cool completely before frosting. (You can speed this up by cooling on a wire rack 20 minutes at room temperature, then transferring to the fridge until cooled.)