Saute leeks in a preheated skillet or soup pot over medium heat until softened. Add the carrots, sugar, parsley, salt, and pepper and saute. Stir frequently.
Add the vegetable broth and increase the heat to high until boiling. Reduce the heat, and simmer covered until the vegetables are very soft.
Using an immersion blender, process the soup to your preferred texture.
Add the dill and stir, serve immediately and garnish with sour cream.