Heat the oil in a 12-inch skillet over moderately low heat. Add the onion and cook until soft, about 10 minutes. Meanwhile, cut each artichoke half into thin wedges (about 6 per half). Return the wedges to the lemon water. When the onion is soft, drain the artichokes and add them to the skillet. Season with salt and pepper and stir to coat them with the fat. Cover and cook until the artichokes are almost tender, 20 to 25 minutes. Check and stir occasionally to be sure they aren't burning or sticking but are steaming steadily; adjust the heat accordingly. If-there's any sticking, add a tablespoon or two of water. Add the peas and cover the pot. Cook until the peas are tender, 3 to 5 minutes. Remove from the heat; stir in the prosciutto and mint. Taste and adjust the seasonings. Serve immediately.