Pat the beef brisket dry with paper towels, then season it evenly on all sides with the kosher salt and freshly ground black pepper.

Heat the olive oil in a large, heavy oven-safe pot or Dutch oven over medium-high heat until shimmering.

Sear the seasoned brisket in the hot olive oil for 4–5 minutes per side, turning as needed, until a deep brown crust forms on all surfaces. Transfer the seared brisket to a plate and set aside.

Reduce the heat to medium and add the thinly sliced yellow onion to the same pot. Cook, stirring often, for about 5 minutes until the onion softens and begins to turn golden, scraping up any browned bits from the bottom.

Stir in the minced garlic and cook for about 30 seconds, just until fragrant, being careful not to let it burn.

Add the tomato paste to the pot and cook, stirring, for 1 minute to lightly caramelize it and deepen its flavor.

Pour in the beef broth and water, then add the Worcestershire sauce, dried thyme, and dried rosemary. Stir well to combine, scraping the bottom of the pot to release all the flavorful browned bits.

Return the seared brisket and any accumulated juices to the pot, nestling it into the liquid and onions. Cover the pot with a tight-fitting lid.

Reduce the heat to low and let the brisket gently simmer on the stovetop for 2 hours, or until it is starting to become tender, maintaining a gentle bubble in the liquid.

After 2 hours of simmering, carefully lift the lid and add the potato chunks and carrot pieces around the brisket, submerging them as much as possible in the cooking liquid.

Cover the pot again and continue to cook on low heat for 60–90 minutes more, or until the brisket is very tender and the potatoes and carrots are soft when pierced with a fork.

Once the brisket and vegetables are tender, transfer the brisket to a cutting board and the potatoes and carrots to a serving dish using a slotted spoon. Tent them loosely with foil to keep warm.

In a small bowl, whisk together the all-purpose flour and cold water until completely smooth to form a slurry with no lumps.

Bring the remaining cooking liquid in the pot to a gentle simmer over medium heat, then slowly whisk in the flour slurry. Continue to cook, whisking, for 3–5 minutes until the gravy thickens to your desired consistency.

Slice the brisket against the grain into thin slices, then arrange the slices on a platter with the cooked potatoes and carrots. Spoon the thickened gravy over the top and sprinkle with the chopped fresh parsley before serving.