Place a rack in the middle of the oven, then preheat the oven to 325ºF.

Season the brisket all over with 1 teaspoon of kosher salt and ½ teaspoon of freshly ground black pepper, then set aside.

In a 7-8-quart Dutch oven with a tight-fitting lid, heat the olive oil over medium-high heat. Add the brisket and sear until well-browned on both sides, about 10 minutes total. Transfer the brisket to a plate and set aside.

To the same pot, add the carrots, celery, onion, and garlic. Reduce the heat to medium and cook, scraping up any browned bits from the bottom of the pot, until the vegetables are beginning to soften and the onion is golden, about 5 minutes. Add the chicken livers (if using) and cook, stirring, until they begin to firm up, about 2 minutes.

Add the wine, stock, tomatoes, bay leaf, and rosemary, then add the seared brisket and any accumulated juices on the plate. Increase the heat to medium high and bring to a simmer, then cover the pot and transfer to the middle rack of the oven. Roast, turning the brisket once halfway through cooking, until fork-tender, 3 to 3½ hours.

Once the brisket is done, transfer it to a cutting board and cover lightly with aluminum foil. Let rest for 15 minutes.

While the brisket rests, skim off and discard any accumulated fat from the surface of the sauce. Using an immersion blender, carefully purée the sauce right in the pot until smooth (you can also transfer it to a blender or food processor to purée, then return it to the pot). Season with salt and pepper to taste, then stir in the parsley.

Slice the rested brisket and serve with the warm sauce on the side. (Alternatively, if making ahead of time, you can slice the brisket, return it to the pot, and refrigerate it overnight. Before serving, remove any solidified fat from the surface of the sauce and reheat, covered, in a 300-degree oven until piping hot.)