Bring the wine and stock to the simmer with the herbs and garlic.
Add the brains, bring to the simmer, and cook uncovered at just below the simmer for 20 minutes.
Allow the brains to cool in the soaking liquid for 20 minutes so they absorb flavor and firm up. Drain them, slice into 1/2" slices and arrange in a serving dish.
Beat the tomato paste into the cooking stock and boil down rapidly until the liquid is reduced to 1 1/2 cups. Take off the burner and beat in the flour-butter mixture; Back on the burner and bring to a boil, stirring, for 1 minute. Salt and pepper as needed.
Arrange the carmelized onions and sauteed mushrooms around the brains and strain the sauce over them. Decorate with croutons and parsley. Serve immediately.
Serve with rice or with parsley potatoes and green beans for a truly french style dish.