Preheat & Prep. To start, preheat oven temperature to 325 degrees F. Line a metal 8x8" baking pan with parchment paper.
Brown Butter. Next, add the butter to a light-colored saucepan and cook over medium heat, stirring constantly, until the butter foams and the butter underneath the foam has deepened to a honey color and the butter smells sweet and fragrant.
Melt Chocolate. Remove the butter from the heat and stir in the chocolate chips. Whisk until the chocolate is totally melted, smooth, and glossy. Let the chocolate cool a few minutes.
Whip Eggs & Brown Sugar. While the chocolate cools, combine brown sugar and eggs in a medium glass bowl. Whisk until the mixture has lightened in color and roughly tripled in volume. This will take 3-5 minutes or so, though you can speed the process by using a hand mixer. The sugar should be completely dissolved--if you rub the mixture between your fingers, there shouldn't be any sugar crystals or grit.
Combine Egg Mixture & Chocolate Mixture. When the eggs/sugar are lighter in color and totally dissolved, whisk the mixture into your cooled chocolate until well combined and incorporated.
Finish Batter. Add vanilla, salt, cocoa powder, and gluten-free flour. Stir with a spatula, until the flour is just barely incorporated. If adding nuts or chocolate chips, fold them in with a spatula at this point.
Bake Brownies. Pour the brownie batter into your prepared baking dish. Bake brownies at 325 degrees F. 22-25 minutes, or until the top is shiny and glossy, and a toothpick inserted in the center comes out with a little bit of mostly done batter. It shouldn't be liquid-y (under-baked) and shouldn't be dry (over-baked)
Cool & Cut. Allow the brownies to cool at least 20-3o minutes before cutting into 12-16 pieces. Feel free to garnish with some flaky sea salt, if desired.
Serve & Store. Enjoy right away or store leftover brownies in an airtight container at room temperature 2-3 days. Or, freeze up to 2 months.