Heat the oven to 350°F/175°C. Line a loaf pan with parchment paper.
Cook the butter over medium heat, stirring constantly, until lightly browned and nutty, 3 to 4 minutes. Remove immediately from the heat.
Pour the butter into a mixing bowl. Whisk in the brown sugar, granulated sugar, egg, yolk, espresso, and vanilla until smooth.
Add the flour, cinnamon, dark chocolate chips, and fine salt. Fold gently just until combined.
Scrape the batter into the prepared pan and smooth the surface. Scatter the chopped chocolate and flaky salt over the top.
Bake until the center is just set and a toothpick inserted shows moist crumbs, 20 to 22 minutes.
Cool completely in the pan, at least 1 hour, before slicing into 14 pieces.