Place the sliced unsalted butter into a light-colored or stainless steel saucepan over medium heat. Melt and cook, stirring occasionally, until the popping subsides and golden-brown specks collect at the bottom. Remove from heat immediately once it smells nutty.

Pour the hot browned butter, including all the toasted brown specks, into a large heat-proof mixing bowl. Add the semi-sweet chocolate chips directly into the hot liquid. Let sit completely undisturbed for one minute, then gently whisk until completely smooth, dark, and glossy. Set aside to cool slightly.

In a separate large mixing bowl, combine the room-temperature eggs, granulated sugar, and vanilla extract. Beat using a hand mixer or heavy-duty whisk for 2 to 3 minutes on medium-high speed until the mixture lightens in color, doubles in volume, and becomes thick and frothy.

While continuously whisking the egg mixture on low speed, slowly stream in the slightly cooled melted chocolate and butter mixture. Mix just until fully combined into a homogeneous batter.

In a small bowl, whisk together the all-purpose flour, dark cocoa powder, espresso powder, and kosher salt. Pour this dry mixture into the wet batter.

Using a rubber spatula, gently fold the ingredients together using a sweeping "J" motion. Stop folding the absolute second you no longer see streaks of dry flour to avoid overmixing.

Pour the batter into a metal 8x8-inch baking pan lined with parchment paper, allowing excess paper to hang over the edges. Smooth the top with the spatula.

Bake in a preheated 350°F (175°C) oven for 28 to 35 minutes. Remove when the edges are set and a toothpick inserted into the center comes out coated in thick, moist, gooey crumbs.

Place the pan on a wire rack and allow the brownies to cool completely in the pan before lifting them out by the parchment paper and slicing.