Prepare the Beef Cheeks: Pat the beef cheeks dry with paper towels and season generously with salt and crushed black peppercorns.

Sear the Meat: In a large, heavy-bottomed pot or Dutch oven, heat the olive oil over medium-high heat. Once hot, add the beef cheeks and sear them on all sides until browned, about 3-4 minutes per side. Remove the cheeks from the pot and set aside.

Caramelize the Onions: In the same pot, reduce the heat to medium. Add the sliced onions and cook, stirring frequently, until they turn golden brown and caramelized, about 15-20 minutes. Add minced garlic and fresh rosemary, cooking for an additional 2 minutes until fragrant.

Deglaze the Pot: Pour in the red wine and balsamic vinegar, scraping up any browned bits from the bottom of the pot. Allow the wine to simmer for about 5 minutes until slightly reduced.

Add Remaining Ingredients: Return the beef cheeks to the pot. Add the beef stock and brown sugar, ensuring the meat is submerged in the liquid. Bring to a gentle simmer.

Braise the Beef: Cover the pot with a lid and reduce the heat to low. Allow the beef cheeks to braise for 3-4 hours, or until the meat is tender and easily pulls apart with a fork. Check occasionally to ensure there is enough liquid; add more stock if necessary.

Finish the Gravy: Once the beef cheeks are tender, remove them from the pot and set aside. Increase the heat to medium-high and reduce the gravy for about 10-15 minutes until it thickens slightly. Taste and adjust seasoning with salt if needed.

Serve: Slice the beef cheeks or serve whole, topped with the silky caramelized onion gravy. Garnish with fresh rosemary sprigs.