Slice the brioche loaf into 8-10 slices and arrange them in a 12-inch round oven-safe baking dish.
In a large mixing bowl, whisk together eggs, milk, sugar, vanilla extract, and espresso powder.
Pour the custard over the brioche slices until they're all covered. Cover and refrigerate for at least 1 hour, preferably overnight.
Bake at 350 degrees Fahrenheit for 30-35 minutes. Note: Bake without the mascarpone topping!
For the Mascarpone Whip: In an electric or stand mixer, combine heavy cream, mascarpone, sugar, espresso, and vanilla. Beat until you get medium peaks - nice and fluffy!
Once the base has cooled completely, spread the whipped topping evenly.
Dust with plenty of cocoa powder and enjoy! Serve at room temperature or cool.