Brains a la Poulette with Mushrooms

Soak some brains in cold water for two hours, remove the sangineous skin enveloping them, and lay them in a saucepan to cook; cover with water, add a dash of vinegar, some sliced carrots and onions, a bunch of parsley garnished with thyme and bay leaf, a clove of garlic, and whole peppers; cook without boiling, letting them barely simmer on the side of the range half an hour; drain on a napkin and cut them lengthwise in four, range in a circle on a dish, and fill up the empty space with mushrooms added to a poulette sauce, pouring a part of it over the brains. Garnish around with triangle-shaped croutons of bread fried in clarified butter, and serve the remainder of the sauce separately.