Adjust an oven rack to the lower-middle position. Preheat the oven to 350F/175C and grease a square 20x20cm baking pan, then line with parchment paper.
Melt the butter and chocolate in a bowl over a saucepan full of boiling water, stirring until melted and smooth. Set aside to cool slightly.
In a small bowl, whisk the flour, baking powder, cocoa powder and salt.
In a large bowl, whisk the eggs, oil, sugars, vanilla and coffee. Add the slightly cooled chocolate mixture and whisk until smooth.
Add the flour mixture, bit by bit, stirring after every addition to combine until all of the dry ingredients have been used. Pour the batter into the prepared pan. Drizzle the peanut butter on top and swirl with a spatula.
Bake for 22-27 minutes, until the sides of the brownies have set, the top is beginning to crackle and look glossy, and a wooden skewer or toothpick inserted into the centre comes out clean. The batter on the skewer should not be wet but should have a good amount of crumbs clinging to it.
Scatter the top with the Maldon sea salt whilst the brownies are still warm, then transfer the pan to a wire rack and let cool completely.
Once cool, gently lift or slide the brownies out of the pan and cut them into squares.