Heat the olive oil in a large Dutch oven over medium-high heat. Add the lamb cubes and brown them on all sides, about 6-8 minutes total. Remove the lamb and set it aside.
Lower the heat to medium. Add the diced onion to the same pot and cook until softened, about 5 minutes. Stir in the garlic and rosemary and cook for 1 minute more.
Sprinkle the flour over the onion mixture and stir for 1 minute to coat everything. Slowly pour in the beef broth while stirring to avoid lumps.
Return the browned lamb to the pot along with the salt and pepper. Bring the mixture to a simmer, then cover and cook on low heat for 45 minutes.
Add the carrots, parsnips, and potatoes to the pot. Stir gently, cover again, and simmer for another 45-60 minutes until the vegetables are tender and the lamb is soft.
Taste and adjust salt if needed. Let the stew rest for 5 minutes before serving.