Preheat your oven to 325°F (160°C). Pat the lamb pieces dry with paper towels — this helps them brown better rather than steaming.
In a large bowl, toss the lamb with olive oil, smoked paprika, cumin, and crushed saffron until evenly coated. Let sit for 10 minutes while you prep the potatoes.
Arrange the potatoes on a sheet tray (I use two standard half-sheet pans), drizzle with a little oil, and season generously with salt. Spread them out in one layer — don't crowd them.
Heat a large Dutch oven or heavy skillet over medium-high heat. Working in batches to avoid crowding, brown the lamb pieces on all sides, about 3-4 minutes per batch. Transfer to a plate as you go.
In the same pot, add the garlic and rosemary, cooking for 30 seconds until fragrant. Return the lamb and any accumulated juices back to the pot along with the sherry vinegar. Stir once, scraping up browned bits from the bottom.
Pour in just enough water (or broth) to come about one-third of the way up the meat — you don't want it swimming, just a shallow simmer. Cover tightly and transfer to the oven.
Roast for 2 hours, checking at the 1½-hour mark to see if it needs more liquid or less. The lamb is done when a fork slides in easily and the meat begins to pull apart slightly.
About 30 minutes before serving, spread the browned potatoes around the edges of the pot, nestling them into the sauce. Let everything cook together for those final minutes so the potatoes absorb flavor.
Remove from oven, season with salt and pepper to taste, and let rest 10 minutes before serving. The sauce will thicken as it cools slightly — this is a good thing.
