Heat the olive oil in a large pot over medium-high heat. Add the lamb chunks, season with salt and pepper, and brown on all sides for about 6 minutes.
Add the sliced leeks and carrot pieces to the pot. Cook for 3 minutes, stirring now and then, until the leeks start to soften.
Pour in the beef broth. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 1 hour until the lamb is tender.
While the stew simmers, make the dumplings. In a bowl, stir together the flour, baking powder, chopped chives, and a pinch of salt. Add the milk and melted butter, and mix just 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 so the dumplings steam properly.
Check the dumplings for doneness by inserting a toothpick. If it comes out clean, the stew is ready to serve.