Preheat your oven to 300°F (150°C). In a small bowl, mix together the garlic, rosemary, thyme, olive oil, salt, and pepper to create a marinade.
Pat the lamb shoulder dry with paper towels. Rub the marinade all over the lamb, ensuring it's well-coated. Let it sit at room temperature for about 30 minutes to allow the flavors to penetrate the meat.
In a Dutch oven or heavy-bottomed pot, heat a tablespoon of olive oil over medium-high heat. Sear the lamb shoulder on all sides until browned, about 8-10 minutes total.
Remove the lamb from the pot and set it aside. Add the red wine to the pot, scraping up any browned bits from the bottom. Let it simmer for 2-3 minutes to reduce slightly.
Stir in the chicken stock, tomato paste, and bay leaves. Return the lamb to the pot, ensuring the liquid comes about halfway up the side of the meat.
Cover the pot with a lid and transfer it to the preheated oven. Cook for 6 hours, turning the lamb halfway through cooking to ensure even cooking.
After 6 hours, check the lamb for tenderness. It should be falling off the bone. If it's not quite there, continue cooking for another 30-60 minutes.
Once done, carefully transfer the lamb to a serving platter. Skim any excess fat from the cooking liquid and strain it to create a smooth sauce. Serve the lamb with the sauce drizzled over the top.