How to Make It
In a small bowl, combine 2 teaspoons of salt and 1 teaspoon of pepper with the thyme, oregano and paprika. Rub the seasonings all over the brisket.
In a medium heatproof bowl, cover the porcini with the hot water and set aside until softened, about 20 minutes. Remove the mushrooms from the soaking liquid; rinse and coarsely chop them. Reserve the soaking liquid.
Preheat the oven to 350°. Heat the oil in a large enameled cast-iron casserole until shimmering. Add the brisket, fat side down, and cook over moderately high heat until well-browned, about 8 minutes per side. Transfer the brisket to a platter and pour off any excess fat from the casserole. Add the vermouth and chicken stock, then pour in the reserved mushroom soaking liquid, stopping before you reach the grit at the bottom. Scrape up the browned bits from the bottom of the casserole and stir in the tomatoes, porcini and bay leaves.
Return the brisket to the casserole, fat side up. Scatter the onions and garlic over the meat and into the liquid and bring to a boil. Cover and cook in the oven for 1 hour. Uncover and cook for 30 minutes. Spoon the onions on top of the brisket and cook for about 30 minutes longer to brown the onions. Push some of the onions back into the liquid, cover and braise for about 2 hours, or until the meat is fork-tender.
Transfer the brisket to a carving board and cover loosely with foil. Simmer the sauce for a few minutes, until it is deeply flavored, then season with salt and pepper. Discard the bay leaves. Carve the brisket across the grain into 3/8-inch thick slices and arrange on a large, warmed platter. Spoon the sauce and onions over the meat and serve.