In a dutch oven set over medium heat, melt the butter. Add the leeks, cabbage, and kale, gently stirring to coat all of them with with the butter. Lower the heat to low, cover and cook about 12 to 15 minutes, or just until the greens are wilted.
Into the dutch oven, add the diced potatoes, broth, and bay leaves. Bring the soup to a simmer and continue cooking/ simmering until the potatoes are softened and falling apart, about 15 to 20 minutes.
Stir in the pepper, cream, and green onions. Use an immersion blender to puree some of the soup for a creamier texture. Ladle the hot soup into bowls and serve with a hunk of crusty bread.