Preheat the oven to 300 degrees.
Soak the dried cepes in hot water with 1/2 teaspoon salt for 30 minutes. Drain, reserving soaking liquid. Rinse cepes under cool running water to eliminate any grit or sand. Strain soaking liquid through coffee filter paper or several layers of damp cheesecloth and set aside.
Wipe caps of fresh mushrooms with damp cloth and a little coarse salt. Set aside.
In a large skillet, heat the fat or oil over medium heat. Add the dried cepes and their soaking liquid and cook until all the liquid in the pan has evaporated. Add the ham, shallots, and garlic and cook, stirring, 1 minute. Add the fresh cepes and cook, stirring, over high heat until all the moisture has evaporated. Pour the wine over the mixture and boil down to a glaze.
Add 1/2 cup hot water and the tomato. Cook, stirrinmg, over gentle heat for an instant, then add 1/2 teaspoon salt, 1/4 teaspoon pepper, and the parsley.
Scrape into an earthenware or enameled cast-iron casserole with a tight-fitting lid. Cover with waxed paper and the lid; cook slowly in the oven 2 to 2 1/2 hours. Uncover and cool completely. Refrigerate, covered.
Reheat slowly. Add the demi glace and adjust seasoning with a few drops of lemon juice, salt, and pepper. Serve with toasted rounds of French bread, if desired.
Suggested Drink: Chateau Magnol, Haut Medoc, Cru Bourgeois 1993
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