Place the court-bouillon in a saucepan, bring to a boil, and add the desalted cod. Poach for 10 minutes, then drain and set aside. Reserve 40 cl of the court-bouillon.
Melt the butter in a large casserole. Add the pearl onions, julienned vegetables, smoked bacon, and mushrooms. Sauté over medium heat until golden brown. Sprinkle with flour, pour in the reserved court-bouillon, and stir well. Season lightly with salt and cracked black pepper, then simmer for 10 minutes.
In a bowl, whisk the heavy cream and egg yolk. Stir this mixture into the casserole without letting it boil.
Adjust the seasoning to taste.
Cut the cod into large cubes and add to the pan to warm through. Transfer to a deep serving dish, sprinkle with chopped parsley, and serve immediately.
For added texture, serve with toasted croutons.
