Coat the bottom of a large pot (ideally a Dutch Oven), with 1½ tablespoons of the olive oil, over medium-high heat. Generously season the lamb with salt and pepper. Once the pot has preheated, add the lamb. Stirring often, cook the lamb just until the pieces are browned on all sides, about 5 minutes. Do not overcrowd the pot — you should do this in two batches.
Add the stock, the onion half and thyme sprigs to the pot. Turn the heat to low, cover, and simmer gently for 1 hour.
While the lamb is cooking, coat the bottom of a large sauté pan with the remaining olive oil, and place it over medium-low heat. Add the carrots, cover and cook until they’re beginning to soften, about 5 minutes. Then add the scallions, garlic greens and garlic, and cook for another couple of minutes, stirring often. Mix in the chard and peas and stir to blend. Continue to sauté just until the chard has wilted, about 2 minutes. Set aside until the lamb has cooked for 1 hour.
Once the lamb has simmered for an hour, remove the onion and thyme sprigs from the pot, and add the vegetable mixture to it. Stir to combine and continue to simmer, covered, until the lamb is very tender, about 15 more minutes.
Season to taste with salt and pepper and serve. (Here's How to Season to Taste.)