Preheat & Prep. To start, preheat the oven temperature to 350 degrees F. Line an 8x8 metal pan with parchment paper.
Brown Butter. In a light-colored medium saucepan, melt butter cook over medium low heat, stirring constantly, until the butter foams and the butter underneath the foam caramelizes and deepens to a honey color and the butter smells sweet and fragrant.
Mix in Chocolate Chips. As soon as you remove the brown butter from the heat, mix in 1 1/2 cups chocolate chips and stir until melted and glossy. Set this mixture aside to cool slightly while you mix the sugar and eggs.
Beat Sugar & Eggs. Add brown sugar, sugar, and eggs to a large mixing bowl. Use a whisk or hand mixer to beat the sugar and eggs 3-5 minutes, or until about tripled in volume and much lighter in color. The sugar should be almost completely dissolved--if you rub the mixture between your fingers, you shouldn't feel almost no grit. Do NOT rush this step or your brownies won't get those nice, glossy tops!
Stir in Chocolate Mixture & Vanilla. Slowly whisk in the melted chocolate/butter mixture and the vanilla extract and stir until smooth.
Add Dry Ingredients. Then, add the gluten-free flour, cocoa powder, and salt and mix until just a few floury patches remain.
Fold In The Mix-Ins. Add 1/2 cup chopped toffee and 1/4 cup chocolate chips. Fold in until just evenly distributed. (The batter will be pretty thick at this point!)
Bake Brownies. Transfer the brownie batter to the prepared pan and smooth out the surface. Bake in the preheated oven 22-24 minutes, or until the tops are glossy, the centers are just set, and a toothpick inserted in the center comes out with moist crumbs attached. (If you prefer a less fudgy brownie, you can add 3-5 minutes to the bake time, but I much prefer these brownies on the fudgy side!)
Top & Cool Brownies. As soon as you remove the brownies from the oven, sprinkle with the remaining 1/2 cup toffee and 1/4 cup chocolate chips. Let the brownies cool completely before cutting into squares. (I recommend chilling them before cutting for the smoothest cuts!)
Serve & Store. Enjoy cooled brownies right away, or store leftovers in an airtight container at room temperature 2-3 days, the refrigerator 3-4 days, or freeze up to 4 weeks.