Preheat your oven to 325°F (165°C) so it is hot and ready for slow braising once the brisket is seared and assembled.
Pat the beef brisket dry with paper towels, then season both sides evenly with the kosher salt and freshly ground black pepper, pressing the seasoning gently into the meat.
Heat the olive oil in a large, heavy oven-safe pot or Dutch oven over medium-high heat until the oil is shimmering but not smoking.
Place the seasoned brisket in the hot pot and sear for 4 to 5 minutes per side, until both sides develop a deep brown crust; remove the brisket to a plate and set aside.
Reduce the heat to medium, add the sliced yellow onions to the same pot, and cook, stirring occasionally, for about 6 to 8 minutes until they soften and turn lightly golden, scraping up any browned bits from the bottom.
Stir in the minced garlic and cook for about 1 minute, just until fragrant, taking care not to let it brown too much.
Add the tomato paste to the onions and garlic and cook, stirring constantly, for 1 to 2 minutes to lightly caramelize the paste and deepen its flavor.
Pour in the beef broth, water, and Worcestershire sauce, then sprinkle in the dried thyme and dried rosemary, stirring well to combine and loosening any remaining browned bits from the bottom of the pot.
Return the seared brisket and any accumulated juices to the pot, nestling it down into the onion and broth mixture so it is mostly surrounded by liquid.
Cover the pot with a tight-fitting lid and transfer it to the preheated oven; braise for 1 1/2 hours (90 minutes) so the brisket begins to become tender.
Carefully remove the pot from the oven, uncover it, and add the Yukon Gold potato chunks around the brisket, gently pressing them down into the braising liquid as much as possible.
Cover the pot again and return it to the oven; continue braising for another 60 to 75 minutes, until the brisket is very tender when pierced with a fork and the potatoes are soft and cooked through.
Take the pot out of the oven and let the brisket rest in the hot liquid for about 10 minutes, then transfer the brisket to a cutting board and slice it against the grain into thick slices.
Arrange the sliced brisket on a serving platter, spoon the potatoes and onions around it, drizzle some of the braising liquid over the top, and sprinkle with the chopped fresh parsley before serving.