Heat the olive oil in a large pot over medium heat. Add the lamb and cook until browned on all sides, about 6 minutes. Remove the lamb and set it aside.
Add the onion and carrots to the same pot. Cook until the onion softens, about 5 minutes. Stir in the garlic and rosemary and cook for 1 minute more.
Return the lamb to the pot. Add the barley, beef broth, salt, and pepper. Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 45 minutes.
While the stew simmers, prepare the dumplings. In a bowl, mix the flour, cheddar cheese, and baking powder. Stir in the milk and melted butter until a soft dough forms.
Drop spoonfuls of the dumpling dough onto the surface of the simmering stew. Cover the pot and cook for 15 minutes without lifting the lid. The dumplings should puff up and cook through.