To the French, grillades are thin pieces of grilled or broiled meat. But to anyone from Creole country or nearby environs, grillades have nothing whatsoever to do with a grill. They’re thin-pounded pieces of tender, milky veal (or eye of round or even pork chops if you prefer), coated in seasoned flour, browned in oil, butter, or bacon grease, then set to simmer in a rich tomato-based sauce. Here the flour from the browned meat helps thicken the sauce as it cooks, although you can certainly play around with filé powder too. It’s dried, pulverized sassafras leaves that, along with okra, helps give extra body to many Creole and Cajun dishes. If the sauce doesn’t look thick enough to your liking, stir in half a teaspoon of filé before adding the mushrooms and parsley. There is one other important distinction to note about Creole grillades: Served over grits, grillades are typically a breakfast or brunch meal. Over rice, they’re dinner.