1. Preheat oven to 425°. Cut shallots in half. Toss together shallots and next 2 ingredients in a jelly-roll pan; sprinkle with desired amount of salt and pepper. Bake 45 to 50 minutes or until shallots are light brown and skins are charred, stirring twice. Cool completely in pan on a wire rack (about 30 minutes). Remove and discard papery skins from shallots and garlic, and coarsely chop shallots and garlic.
2. Stir together sour cream and next 7 ingredients; fold in shallot mixture. Add salt and pepper to taste. Cover and chill 4 to 48 hours. Stir before serving. Add salt and pepper to taste just before serving, if desired.
Make Ahead: Prepare recipe up to 2 days in advance; chill in airtight container. Let stand at room temperature 30 minutes before serving.