Season the beef brisket on all sides with the kosher salt and freshly ground black pepper, pressing the seasoning gently into the meat.
Heat the olive oil in a large, heavy-bottomed oven-safe pot or Dutch oven over medium-high heat until shimmering.
Place the seasoned brisket into the hot pot and sear for about 4–5 minutes per side, until a deep brown crust forms; transfer the seared brisket to a plate and set aside.
Reduce the heat to medium, add the sliced yellow onion to the same pot, and cook, stirring occasionally, for 5–7 minutes until softened and lightly golden.
Stir in the minced garlic and cook for 30–60 seconds, just until fragrant, being careful not to let it burn.
Add the tomato paste to the pot and cook, stirring, for 1–2 minutes to lightly caramelize it and deepen its flavor.
Pour in the beef broth, water, and Worcestershire sauce, stirring well and scraping up any browned bits from the bottom of the pot.
Sprinkle in the dried thyme and dried rosemary, stir to combine, and bring the mixture to a gentle simmer.
Return the seared brisket and any accumulated juices to the pot, nestling it into the onion and liquid mixture.
Cover the pot with a tight-fitting lid, reduce the heat to low, and let the brisket simmer gently on the stovetop for about 3–3 1/2 hours, turning once or twice, until very tender and easy to pull apart with a fork.
About 40 minutes before the brisket is finished, place the peeled and chunked russet potatoes into a large pot and cover with cold water by about 1 inch.
Add a generous pinch of salt to the potato pot, bring to a boil over medium-high heat, then reduce to a gentle boil and cook for 15–20 minutes, until the potatoes are very tender when pierced with a fork.
Drain the potatoes well, return them to the warm pot, and let them sit for 1–2 minutes to allow excess moisture to evaporate.
Add the unsalted butter for the mashed potatoes to the hot potatoes and mash until mostly smooth.
Pour in the warmed whole milk and add the sour cream, then continue mashing or whipping until the potatoes are creamy and smooth.
Season the mashed potatoes with the kosher salt for the potatoes and the freshly ground black pepper for the potatoes, tasting and adjusting if needed; cover to keep warm.
Once the brisket is very tender, transfer it to a cutting board and loosely cover with foil to rest for 10–15 minutes.
Bring the remaining cooking liquid and onions in the pot to a gentle simmer over medium heat and let it reduce for about 5–10 minutes to slightly thicken and concentrate in flavor.
Stir the unsalted butter for the brisket sauce into the hot reduced liquid until melted and glossy, then taste and adjust seasoning if desired.
Slice the rested brisket against the grain into thin slices, or gently pull it into large pieces if it is very tender.
To serve, spoon a generous mound of mashed potatoes onto each plate, top with slices or pieces of brisket, and ladle some of the onion-rich sauce over the top.
Garnish each serving with the chopped fresh parsley if using, and enjoy the brisket and mashed potatoes while hot.