In a braiser or sauté pan large enough to hold all the lamb, sauté the sliced onion in a olive oil over a gentle flame until tender and translucent. Raise the heat a bit and add the lamb pieces, turning them so they brown on all sides, taking care so the onion doesn't burn. Season with salt and pepper as you go.

Add a splash of white wine, give the pan a stir, and let the wine cook off. Add a ladleful of water, stir again, and cover tightly. Turn the heat way down, so that the lamb braises gently. Let it cook this way until the meat is perfectly tender, usually about 45 minutes. The liquid should have reduced considerably but not completely evaporated; check on the meat from time to time; add more water if needed to keep things moist.

If using fresh peas: Shell the peas and add them about halfway through the braise, so they, too, will be perfectly tender when the meat is.

If using frozen peas: Add them when the meat is almost tender, along with another ladleful of water if needed, and let them braise with the meat for the last 5-10 minutes, until they, too, are tender and have lost a bit of their bright green color.

To finish the dish, beat the eggs and grated cheese together (and if you like, a bit of minced parsley) in a bowl. Take the pan off the flame entirely, and pour over the egg and cheese mixture, and mix it well but gingerly with the lamb and peas, turning until the eggs have set enough to form a creamy sauce. Serve immediately.