Make the brownies:
Position a rack in the center of the oven and heat the oven to 375°F. Line 6 standard-size muffin cups with cupcake liners.
In a 4-cup Pyrex measuring cup, microwave the butter on high until melted and very hot, 60 to 90 seconds. Add the chocolate to the melted butter and microwave on high for 30 seconds; let stand 1 minute. Stir until the chocolate is completely melted and smooth, heating more, if necessary, in 15 second bursts.
Whisk the espresso powder, vanilla, and salt into the chocolate mixture. Whisk in the brown sugar until it begins to dissolve, about 30 seconds. Whisk in the egg until the mixture is thick and smooth, 30 to 45 seconds. Whisk in the stout and then the flour until the mixture is completely smooth, about 30 seconds.
Portion the batter evenly among the prepared muffin cups, filling each three-quarters full. Bake until the centers are barely set and a tester inserted in the center comes out with moist crumbs, 15 to 20 minutes. Transfer to a rack to cool slightly.
Make the sauce:
Meanwhile, in a heavy-duty 1-quart saucepan, boil the stout over high heat until reduced by half, 3 to 4 minutes. Remove from the heat. Add the chocolate and sugar; let stand 1 minute. Add the cream and whisk until smooth.