Trim thick fat from the lamb, cut into 1½-inch cubes, and pat very dry with paper towels. Toss with 1 teaspoon salt, ½ teaspoon pepper, and the flour until every cube has a thin, even dusting. Dice the onions, slice the celery, and mince the garlic; keep them together. Halve the potatoes and cut the carrots into 1-inch chunks; keep these separate. Chop the parsley and set aside.
Heat 1 tablespoon olive oil in the Dutch oven over medium-high. Brown half the lamb in a single layer, about 6 minutes total, turning to brown all sides. Transfer to a plate and repeat with 1 more tablespoon oil and the remaining lamb. Lower the heat to medium if the browned bits smell burnt.
Reduce heat to medium and add the remaining 1 tablespoon olive oil. Cook the onions and celery for about 6 minutes, scraping the bottom of the pot, until soft and translucent. Stir in the garlic for 30 seconds, then add the tomato paste and stir constantly for 1 to 2 minutes until it darkens to brick red and smells sweet.
Pour in the red wine and scrape the bottom of the pot firmly to loosen every browned bit. Simmer for 3 to 4 minutes until the wine has reduced by about half and the sharp alcohol smell has faded.
Return the browned lamb and any collected juices to the pot. Add the beef broth, Worcestershire sauce, bay leaves, thyme, rosemary, remaining ½ teaspoon salt, and remaining ¼ teaspoon pepper. Bring to a bare boil, then lower the heat to its lowest setting with the lid slightly ajar. Simmer for 60 minutes, stirring every 20 minutes; the surface should show only a few lazy bubbles.
Stir in the potatoes and carrots, pushing them into the liquid, and add up to ½ cup water or broth if they are not mostly covered. Return to a gentle simmer with the lid slightly ajar and cook for 30 minutes, until a fork slides easily into the potatoes and a lamb cube pulls apart with almost no resistance. Continue simmering in 10-minute increments if the lamb is still chewy.
Stir in the frozen peas and simmer for 5 minutes, until bright green and heated through. Remove the bay leaves and herb stems with a slotted spoon, skim any visible fat from the surface, and taste the gravy for salt and pepper. Ladle into warm bowls and sprinkle each serving with chopped parsley.