Sort through the green lentils, rinse them thoroughly under cold running water, and drain. Roughly chop the carrot and onion and peel the garlic.
Heat 2 tablespoons of olive oil in a large pot over medium heat. Add the onion, carrot, and garlic. Cook for 7–8 minutes, stirring occasionally.
Add the paprika, turmeric, and ground ginger. Stir and cook for about 30 seconds, until fragrant.
Add the green lentils and pour in 5 cups of hot broth. Bring to a boil.
Reduce the heat, partially cover the pot, and simmer for 35–45 minutes, until the lentils are completely tender. Stir occasionally and add water as needed.
Pour in the light cream or half-and-half. Season with salt and heat gently without bringing the soup to a hard boil.
Purée the soup with an immersion blender until smooth or slightly textured.
If the soup is too thick, gradually stir in additional hot water or broth. Taste and adjust the seasoning.
Ladle the soup into bowls. Top with chickpeas and chopped parsley. If desired, mix the harissa with olive oil and drizzle it over the soup.