Add onions and garlic to lightly greased saucepan and cook, covered, over medium-low heat until wilted, about 8 to 10 minutes.
Stir in sugar and continue to cook uncovered until onions are lightly browned. Stir in flour; cook about 1 minute longer. Add broth and herbs; heat to boiling. Reduce heat and simmer, covered, 30 minutes. Discard bay leaves.
Process half the soup in food processor or blender until smooth. Return to saucepan and season to taste with salt, cayenne, and white pepper.
Serve warm, or chilled, sprinkle each bowl of soup with chives.