Preheat & Prep. To start, preheat oven to 350 degrees F. Line an 8x8 metal baking pan with parchment paper.
Melt Butter & Chocolate. In a medium microwave-safe bowl, combine butter cubes and chocolate chips. Melt in 15-20 second increments, stirring in between each interval, until the chocolate mixture is smooth. (Alternatively, you can do this in a small saucepan on the stove over low heat)
Add Nutella to Chocolate Mixture and stir until smooth. This may take a minute, but keep at it until the mixture is even!
Beat Sugar & Eggs. In a large bowl, combine granulated sugar, eggs, and egg yolk. Beat with a whisk or hand mixer 2-4 minutes, or until the mixture is much lighter in color and the sugar is fully dissolved. (If you rub this mixture between your fingers, there shouldn't be any grit. Don't rush this or your brownies won't have glossy tops!) Mix in the vanilla extract.
Combine Chocolate & Egg Mixtures. Add the chocolate mixture to the egg/sugar mixture and mix until evenly blended.
Add Dry Ingredients. Then, add gluten-free flour, cocoa powder, and salt. Mix until just combined. The batter will be thick and sticky!
Transfer Batter To The Pan and use an offset spatula to spread the brownie batter into an even layer. To create the swirl, measure 1/3 cup Nutella and use a spoon to scoop 5-7 small dollops of Nutella around the surface of the brownie batter. (Think of creating dots on a dice--you want to spread the dollops out fairly evenly with space in between--I do 5 dots like the dots on a dice, then fill in the other spaces with 4 smaller dots.) Use a thin knife to gently swirl the Nutella into the surface of the brownie batter. Less is more here so you have visible swirls!
Bake Brownies. Add brownies to the preheated oven and bake 23-25 minutes. (Err on the side of underbaking for fudgy brownies!) Place the pan on a wire rack to let the brownies cool. If desired, you can garnish the brownies with a sprinkle of flaky salt.
Cool COMPLETELY Before Slicing. For best results, let the brownies cool completely before slicing. (You can even chill them for perfectly neat slices) Cut into 9 large brownies, 12 medium size brownies, or 16 small brownies.
Serve & Store. Enjoy after slicing and store leftover brownies in an airtight container at room temperature 1-2 days, 3-4 days in the refrigerator, or 2 months in the freezer.