Cut the round steaks into 3-inch squares. Season with salt and cracked pepper. Dust the pieces generously with the flour.
In a large cast iron Dutch oven, melt the shortening over medium-high heat. Brown the meat (in batches, if necessary) on all sides. Add the onion, celery, bell pepper, tomatoes, scallions, and garlic and cook, stirring, until the vegetables are wilted, 3 to 5 minutes. Pour in the stock and bring to a low boil; reduce the heat to a simmer. Cover the pot and cook the grillades slowly for about 45 minutes, stirring occasionally to prevent scorching.
When the meat is tender, stir in the mushrooms and parsley. Adjust the seasonings, if necessary. Cook for 10 minutes, then serve over grits or rice.