Heat the oven to 350°F and coat a 9x9 baking dish with cooking spray. A light-colored metal pan encourages even baking and helps the corners stay tender.
Place the butter pieces and the 1/2 cup (85g) semi-sweet chocolate chips in a large microwave-safe bowl, then microwave for 30 seconds. Stir thoroughly, then continue heating in 15-second bursts and stirring after each burst until the mixture is fully melted and glossy.
Whisk the brown sugar and granulated sugar into the warm chocolate-butter mixture for 1 minute. The mixture should look slightly lighter, thicker, and shinier as the sugar begins to dissolve.
Add the eggs one at a time, whisking each for 20 seconds before adding the next, then whisk in the egg yolk, vanilla, espresso powder, and salt. The batter should become smooth and ribbony, with no streaks of egg remaining.
Use a rubber spatula to fold in the cocoa powder and gluten-free flour until no dry patches remain, then fold in the chocolate chips. Stop mixing as soon as the batter looks uniformly dark and thick to keep the brownies dense.
Spread the batter evenly in the prepared pan and bake for 30 to 35 minutes. The edges should look set and pull away slightly from the pan, while a tester in the center should show moist crumbs but no wet batter.
Let the brownies cool in the pan for 30 minutes before slicing. The center firms as it cools, giving you cleaner cuts and a fudgier texture.