First make the brownie layer: Line an 8-inch square baking dish with parchment paper, and preheat the oven to 325-degrees F.
In a saucepan, melt the butter over medium-low heat. Make sure it doesn’t brown, sputter or melt too quickly. Nice and slow..
Remove the butter from the heat, and stir in the cocoa powder, and sugar. Stir very well to combine. It will be grainy.
Next, stir in the vanilla and salt. Stir for about a minute, to release most of the heat from the mixture. It should be warm to the touch, but not hot. If it’s still hot, let it rest on the counter for a few minute before proceeding to the next step.
Whisk in the eggs one at a time until well-blended. Next, stir in the flour. Stir the flour very very well, at least 50 strokes.
Scrape the brownie mixture into the pan (it’s very thick), spread it evenly and bake for 25-29 minutes, until the brownies are dry and shiny on top and a toothpick inserted comes out with moist crumbs but no overly wet batter.
Let the brownies cool completely! Meanwhile, melt the ice cream and soften the cream cheese.
When the brownies are totally cool, make the tiramisu topping: combine the melted coffee ice cream, softened cream cheese, powdered sugar, and espresso powder in a bowl. Beat with an electric mixer until fluffy.
Scrape this mixture over the brownies, and chill for at least an hour. You can do this overnight, too. Before serving, dust with cocoa powder, cut into squares and serve.