Place beef in ziplock baggie. Pour in stout, squeeze out air and seal bag. Place in bowl and refrigerate for 36-48 hours.
Remove beef from marinade, reserving marinade. Pat beef dry. Place in bowl and toss with flour, coating evenly.
In large Dutch oven, render bacon lardons until medium brown. Remove from pot and reserve.
Brown beef in batches to avoid crowding. Add olive oil to bacon renderings if necessary with each batch. Remove each batch to clean bowl.
Lightly brown mushrooms but not to the point where they release fluids. Remove to plate and reserve.
Brown onion and garlic with the smashed anchovy fillets until golden but not crisped. Add ½ cup reserved marinade to pot and deglaze, scraping browned bits from bottom and sides.
Return beef and mushrooms to pot. Add Worcestershire sauce, tomato paste, beef stock and remainder of reserved marinade.
Add herbs to pot. Stir gently to combine.
Simmer covered on stove top for 2.5 hours, stirring occasionally. Remove lid and continue cooking an additional 30 minutes to thicken stew until it coats the back of a spoon.
For Pastry Crust: Heat oven to 400°F.
Roll pastry crust on floured surface. Cut into individual rounds to place atop ramekins.
Mix egg and water in small bowl.
Gently place pastry on top of each ramekin. Brush with egg/water mixture.
Bake in oven for 30 minutes or until golden and has puffed up a bit.
