Melt the chocolate and butter together in the microwave in short intervals, stirring until smooth. Add the brown sugar, eggs, vanilla, and dissolved coffee, whisking until glossy and fully combined. Fold in the flour and cocoa powder just until no dry spots remain. Scrape the batter into the prepared pan and sprinkle lightly with coarse sea salt.

Bake until the center is just set and a tester comes out with moist crumbs, about 20 minutes. Cool completely in the pan.

To make the caramel, cook the sugar in a small skillet over medium heat until melted and amber. Gradually add the water, stirring until smooth, then add the butter and cook briefly until glossy. Remove from heat.

Drizzle the caramel over the cooled brownie, finish with a light pinch of coarse sea salt, and slice.