Heat oil over medium heat in a large stockpot or Dutch oven. Add lamb pieces and cook, stirring gently, until evenly browned. Season with salt and pepper.
Add the onion, carrots, and parsnips and cook gently alongside the meat for a few minutes. Stir in the water. Cover and bring to a boil before turning the heat down to low. Simmer for 1 hour or longer, depending on the cut of meat you used and if it is tender yet.
Stir in potatoes, and simmer for 15 to 20 minutes, before adding leeks and rosemary. Continue to simmer uncovered, until potatoes are tender but still whole. Serve piping hot in bowls garnished with fresh parsley.