Preheat your oven to 325°F (165°C).

In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Season the lamb shoulder generously with salt and black pepper. When the oil is hot, add the lamb and sear on all sides until browned, about 5-7 minutes per side. Remove the lamb from the pot and set aside.

In the same pot, add the quartered red onions and smashed garlic. Sear them until they are charred and caramelized, about 5-10 minutes.

Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom. Let it simmer for about 3-5 minutes until slightly reduced.

Return the lamb to the pot. Add the chicken or beef broth and wild savory. Bring the mixture to a simmer.

Cover the pot with a lid and transfer it to the preheated oven. Braise for 3-4 hours, or until the lamb is fork-tender.

While the lamb is braising, bring a pot of salted water to a boil. Add the diced turnips and cook until tender, about 15-20 minutes. Drain and transfer to a blender.

In the blender, add the heavy cream, butter, salt, and pepper to the cooked turnips. Blend until smooth and velvety. Adjust seasoning if necessary.

Once the lamb is done, remove it from the oven and let it rest for 15 minutes. Slice the lamb and serve it on a platter with the turnip gravy drizzled over the top. Garnish with fresh herbs if desired.