Heat the olive oil in a large pot over medium heat. Add the lamb cubes and brown them on all sides, about 6 minutes. Season with salt and pepper, then remove the lamb to a plate.
Add the onion to the same pot and cook until softened, about 5 minutes. Stir in the garlic, cinnamon, and cumin and cook for 1 minute more.
Return the lamb to the pot along with the eggplant cubes. Stir to coat everything in the spices.
Pour in the lamb broth and add the crushed cardamom pods. Bring to a simmer, then cover and cook on low heat for 45 minutes.
Stir in the prunes and continue simmering uncovered for 15 minutes, until the lamb is tender and the sauce has thickened slightly.
While the stew finishes, spread the walnuts on a baking sheet and toast them in a 350°F oven for 8 minutes. Let them cool, then chop roughly.
Remove the cardamom pods from the stew. Ladle into bowls and top each serving with the toasted walnuts and chopped parsley.