Season the chuck roast on both sides with salt and black pepper. Heat oil In a large Dutch oven over medium-high heat. Once hot, sear the roast on both sides for 2-3 minutes each.
Directly to the Dutch oven, add the beef consommé, beef broth, cream of mushroom soup, salt, pepper, garlic powder, onion powder, and herbs de Provence. Add enough water to nearly cover the roast and stir to combine. Bring to a boil, then reduce the heat to medium-low. Cover and simmer for 2 to 2 1/2 hours, until the roast is fall-apart tender.
Leaving the broth in the Dutch oven, carefully transfer the roast to a large bowl and shred with two forks.
To make the dumplings, in a medium bowl, whisk together the self-rising flour, all-purpose flour, and black pepper. Working quickly, grate the chilled butter on a box grater, add to the flour mixture, and gently toss until coated.
Make a well in the center and add the milk. Use a spatula to fold until a dough just forms. If the dough seems too dry, add additional milk, 1 tablespoon at a time.
Lightly flour a clean work surface and using a rolling pin, roll the dough out to 1/4 inch thick. Using a butter knife or pizza cutter, cut into 1-inch squares. If desired, sprinkle the cornmeal evenly over the dough and gently pat to adhere.
Whisk together 1 to 2 tablespoons cornstarch with 2 to 3 tablespoons cold water until smooth. Stir the slurry into the simmering broth.
Return the broth to a boil over medium-high heat, then reduce the heat to medium. Drop the dumplings into the broth one at a time, then raise the heat to return the broth to a boil. Reduce the heat to low and simmer until the dumplings are cooked through and the mixture has thickened, about 10 minutes.
Season with salt and freshly ground black pepper to taste and serve immediately.