In a large soup pot, heat the olive oil over medium-high heat. Add the onions and cook, stirring occasionally, until softened, about 7 minutes. Tie the basil sprigs together with a piece of kitchen twine. Add the basil, tomatoes, chicken stock, 1-1/2 tsp. salt, and 1/2 tsp. pepper to the onions. Bring to a boil over high heat, reduce the heat to medium low and let simmer until reduced by one-quarter, about 20 minutes. Let cool. Remove the basil sprigs.
In a blender, purée the soup in batches until very smooth, at least 3 min. Strain the soup into a clean pot and bring to a simmer over medium heat. Remove from the heat; stir in the cream and balsamic vinegar. Taste and add salt and pepper if needed. Just before serving, cut the basil leaves into very thin slices. Ladle the hot soup into bowls and garnish with the fresh basil.
nutrition information (per serving):
Photo: Rita Maas