Pat the lamb shanks dry and season them generously with salt and pepper on all sides.
Heat the olive oil in a large Dutch oven over medium-high heat. Brown the shanks in batches until they develop a deep color on all sides, then remove them to a plate.
Lower the heat to medium and add the diced onion to the same pot. Cook until softened, then stir in the minced garlic for one minute.
Pour in the beef broth and apple cider, scraping the bottom of the pot to release any browned bits. Return the shanks to the pot along with the rosemary and thyme sprigs.
Bring the liquid to a gentle simmer, cover, and cook for one hour.
Add the cubed butternut squash and chopped apples. Continue simmering uncovered for another 45 to 60 minutes until the lamb is very tender and the squash is soft but not falling apart.
Taste the broth and adjust salt and pepper as needed. Remove the herb sprigs before serving.