Preheat the oven to 375 degrees F. Line a 15-by-10-inch rimmed baking sheet with parchment paper.
Combine the butter and chocolate in a medium microwave-safe bowl. Microwave the mixture for about 45 seconds and then check; you want it mostly melted with a few small chunks. Stir and continue to microwave in 15-second intervals if necessary.
Stir the chocolate mixture until relatively smooth, then stir in the coffee. Stir in the sugar, then then the vanilla, and then the egg. Mix well. Add the salt and flour and mix until just smooth.
Spread the batter on the prepared baking sheet with a rubber spatula. Bake for 30 minutes. Cool completely.
Cut the brownie into strips or into shapes with cookie cutters. Devour with ice cream, or serve as bite-size treats.