Prepare the pan: Heat the oven to 175°C. Line a greased 8x8 metal pan with parchment paper.
Brown the butter: Melt the cubed butter in a saucepan over medium heat. Continue cooking and stirring until the foam settles and the milk solids turn golden brown. Remove from the heat.
Make the chocolate mixture: Stir the chopped chocolate into the brown butter until smooth. Whisk in the oil and cocoa powder, then cool for several minutes.
Mix the batter: Whisk the eggs, egg yolk, and granulated sugar. Add the powdered sugar, vanilla, and salt. Whisk in the chocolate mixture, then fold in the flour, espresso powder, and chocolate chips.
Bake: Spread the batter in the prepared pan and bake for 29 to 32 minutes, until the edges are set and the center has a slight wobble.
Cool and slice: Cool in the pan for at least 80 minutes. For neat slices, chill briefly and wipe a sharp knife between cuts.