Using an immersion blender or traditional blender, puree until very smooth, 30 seconds to 1 minute. To ‘clean’ the canister, pour in a little half-and-half, blend briefly, then add to the soup. Return to pan (or a soup pot); add enough half-and-half so the mixture is souplike, yet thick enough to float garnish. Taste, and add salt and pepper if needed. Heat through, ladle into bowls, garnish and serve.