In the bowl of a stand mixer fitted with a dough hook add the flour, sugar and yeast.
Add the beer to a microwave safe bowl, microwave on high for 30 seconds, test temperate and repeat until beer reaches between 120F and 130F.
Add the beer to the stand mixer, mix until most of the flour has been moistened.
Add the vanilla then the yolks, one at a time. Add the cream, and salt.
Building up speed, beat on high until the dough comes together and gathers around the blade.
The dough will be very soft.
Add dough to a lightly oiled bowl, cover and allow to sit at room temperature for 1 hour or until doubles in size.
Punch down the dough and knead lightly to remove any air bubbles.
Add the dough to a lightly floured surface. Pull into a large rectangle about ½ inch thick. Use a 3-inch round cutter to cut out 12 cricles. Allow to rest until doubled in size, about 30 minutes.
Heat 4-inches of oil in a pot over high heat until the oil reaches 350F on a deep fry thermometer. Adjust heat to maintain that temperature. A few at a time, fry the circles until golden brown on both sides, about 2 minutes.
Remove and add to a wire rack.
Set out three medium sized bowls.
Separate the eggs, adding the yolks to one bowl and the whites to another bowl.
Add a pinch of salt to the whites, beat until stiff peaks form. Add 2 tablespoons white sugar, beat until well combined.
Add the remaining 2 tablespoons white sugar to the yolks, beat until light in color and ribbony. Beat in the mascarpone then 2 tablespoons stout beer to the yolks.
Add the cream and ¼ cup powdered to the remaining bowl, beat until soft peaks form. Stir the whipped cream into the mascarpone then gently fold in the egg whites until just combined.
Add cream to a large piping bag with a metal tip and a pea-sized opening.
One at a time make a small slit in the side of the doughnuts.
Press the metal tip into the side of the doughnuts, pipe the filling into each doughnut adding about 2 tablespoons of cream to the center of each dough nut.
In a shallow bowl combine the remaining powdered sugar, espresso powder and beer, stir until well combined and thick.
One at a time gently dip the doughnuts into the glaze, sprinkle with chocolate and return to the wire rack until set. Serve immediately.