In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the lamb cubes and brown them on all sides, about 5-7 minutes. Remove the lamb and set aside.
In the same pot, add the chopped onion and sauté until translucent, about 3-4 minutes. Add the minced garlic and cook for an additional minute.
Return the browned lamb to the pot. Pour in the broth and bring to a boil.
Add the diced potatoes, sliced carrots, chopped celery, thyme, rosemary, salt, and pepper. Stir to combine.
Reduce the heat to low, cover, and let simmer for about 1.5 to 2 hours, or until the lamb is tender and the vegetables are cooked through. Stir occasionally.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.