In a large soup pot over medium-high heat, add potatoes, carrots, onion, and vegetable or chicken broth. Cover and simmer 15 to 20 minutes or until vegetables are tender when pierced with a fork. Remove from heat and let slightly cool.
While vegetables are cooking, make the cream sauce - In a medium saucepan over medium-high heat, melt butter; add flour, stirring constantly until mixture is smooth and bubbly. Add milk and bring to a boil, stirring constantly, until thickened. Remove from heat. Add cheddar cheese and dill weed. Stir until cheese is melted. Set aside.
In a food processor or blender, in small batches, puree potato mixture with some of the milk. Pour blended potato mixture back into the soup pot. Add the cheese sauce, sour cream, remaining milk, salt, pepper, and chili pepper. Stir until thoroughly blended. Return to medium heat and heat until warm. Remove from heat and serve in soup bowls.
Makes 6 servings.