Melt butter in heavy large pot over medium heat. Add leek and garlic; sauté until tender but not brown, about 4 minutes. Add potatoes and carrots; sauté 5 minutes longer. Add chicken broth and dill; simmer uncovered until vegetables are tender, about 20 minutes. Remove from heat.
Add milk to soup. Transfer half of soup to blender. Add cream cheese and blend until smooth. Return soup to pot. Add 1 cup grated sharp cheddar cheese and stir over low heat until melted. Season soup to taste with salt and pepper. (Can be made 1 day ahead. Chill. Bring to simmer before serving.) Transfer to large serving bowl. Garnish soup with chopped fresh parsley and additional grated sharp cheddar cheese, if desired.
Makes 8 first-course or 4 main-course servings.