Preheat your oven to 350°F (175°C).
Heat olive oil in a Dutch oven over medium-high heat. Brown the lamb shanks on all sides, then remove and set aside.
Add the chopped onion to the pot and cook until softened. Add the garlic and cook for another minute.
Pour in the beef broth and beer, then stir in the tomato paste, thyme, and rosemary. Season with salt and pepper.
Return the lamb shanks to the pot. Bring to a simmer, then cover and transfer to the preheated oven.
Bake for about 3 hours, or until the meat is tender and falling off the bone.
Remove the lamb shanks from the pot and keep warm. Skim any excess fat from the sauce and simmer until slightly thickened.
Serve the lamb shanks with the sauce spooned over the top.