Season lamb with salt and pepper. In a large Dutch oven or heavy pot, cook lamb over medium until some of the fat has rendered, about 4 minutes. Increase heat to high and cook, stirring occasionally, until lamb is browned on all sides, 4 minutes. Add leeks and cook, scraping up any browned bits from the bottom of the pot, until leeks are translucent, 4 minutes. Add broth.
Bring mixture to a boil. Reduce heat and simmer, partially covered, 45 minutes. Add potatoes and cook until potatoes and lamb are tender when pierced with a knife, 15 minutes. Season to taste with salt and pepper. To serve, top with parsley.
Prepare this dinner start to finish on Sunday, refrigerate, then reheat gently to serve.