Preheat the oven to 350°F (180°C).
In a large Dutch oven or a deep ovenproof skillet with a lid, heat the oil over medium-high heat until sizzling hot. Season the lamb generously with salt and pepper to taste. Cook until brown, about 5 minutes per side. Place the lamb on a plate.
Reduce the heat to medium, add the onion to the same skillet, and cook, stirring, until the onion is tender and lightly browned, about 5 minutes. Add the thyme and wine and scrape up any brown bits from the bottom of the pan.
Return the lamb to the pan and add enough water to cover about 2/3 of the way up the lamb. Bring the liquid to a low boil. Cover the pan tightly and place in the oven, undisturbed, until the lamb is fork-tender, about 2 1/2 hours.
Remove the pan from the oven. Remove the lamb from the liquid (reserving the liquid) to cool slightly. Pull the lamb off the bones in large chunks. You should have about 4 cups cooked meat. (This can be done several days in advance. Store refrigerated in the liquid. The fat will rise to the top and you can skim it off after it has cooled completely.)
In a large skillet over medium-high, heat 2 tablespoons butter and the olive oil until sizzling hot. Reduce the heat to medium and add the onion and cook, stirring often, until soft, about 5 minutes.
Sprinkle 2 to 4 tablespoons flour (the more flour you add, the thicker the consistency of the resulting stew) over the onion and continue to cook, stirring constantly, another 2 minutes.
Slowly add the second cup of wine and scrape up brown bits from the bottom of the pan. Whisk in the broth or reserved cooking liquid, about 1/2 cup at a time, and bring to a low boil, whisking constantly. It may be necessary to add a little more stock or water to achieve the desired consistency. Stir in the tomato paste to mix, reduce the heat to simmer, and cook about 10 minutes.
Add the lamb, thyme, parsley, carrots, and peas, and continue to cook until the carrots are tender, about 20 minutes. Season with salt and pepper to taste. (For best results, make the stew a day in advance, let it cool, cover, and refrigerate it overnight. Then gently rewarm over low heat prior to proceeding. This allows the flavors of the stew to meld and play nicely with one another.)