Preheat oven to 400°F. Place bell pepper, carrot pieces, and green onions on a rimmed baking sheet. Roast vegetables for 15 minutes, removing the green onions after 10 minutes. Let cool.
Put the vegetables in a food processor, peeling off the pepper skin if you wish. (It will peel off easily once cooled.) Pulse vegetables until they are chopped into small pieces.
Pulse in the sour cream, cream cheese, salt, and pepper until well blended.
Cover and chill for up to 3 days. To serve, stir dip. Serve with vegetables or crackers.