Preheat the oven to 325°F (160°C). Gather a Dutch oven or a flameproof casserole with a lid.
Pat the lamb chunks dry with paper towels if needed. Put the 3 tablespoons all-purpose flour in a shallow bowl or plate and toss the lamb in the flour until evenly coated. Season the floured lamb lightly with kosher salt and freshly ground black pepper.
Heat 3 tablespoons extra virgin olive oil in the Dutch oven over medium-high heat until shimmering.
Working in batches to avoid crowding, add the lamb to the hot oil and brown on all sides, turning as needed (about 4–6 minutes per batch). Transfer browned lamb to a plate and set aside. Wipe out excess oil only if the pan is smoking; otherwise leave the fond (browned bits) in the pot.
Add the 3 large peeled and thickly sliced carrots and the 3 peeled and quartered medium onions to the pot. Stir and cook over medium heat for 3–5 minutes, scraping the bottom of the pot to loosen browned bits. Season the vegetables with salt and pepper to taste.
Return the browned lamb and any accumulated juices to the pot. Pour in 2 cups lamb or chicken stock and stir to combine, again scraping up any browned bits from the bottom of the pot. Bring the mixture to a gentle boil on the stovetop.
Add the 8 peeled and halved medium potatoes to the pot. Season again with salt and pepper to taste. Place the 2 sprigs fresh thyme on top of the stew.
Cover the Dutch oven with its lid and transfer it to the preheated oven. Bake for about 2 hours, or until the lamb is very tender and the potatoes are cooked through.
Remove the pot from the oven, discard the thyme sprigs, taste and adjust seasoning if needed, then sprinkle with 1 tablespoon chopped fresh Italian parsley and 1 tablespoon chopped chives before serving.
Notes
Lamb options:Use lamb stew meat (already chopped). Or cut up lamb shoulder and use that.