Heat olive oil in a large pot over medium heat. Cook and stir leeks and carrots in hot oil until softened, 5 to 10 minutes.
Stir chicken broth into leek mixture; bring to a boil. Add potatoes, salt, cloves, and pepper; boil until potatoes are tender, about 15 minutes.
Pour pumpkin puree into a large bowl. Stir 1 cup of broth and potatoes mixture into pumpkin.
Pour pumpkin mixture, corn, and milk into chicken broth mixture in the large pot. Stir to combine and simmer until heated through and flavors blend, at least 5 minutes. Sprinkle individual servings with parsley.