This is adapted from the Sunday Soup cookbook. This is my husband's favorite soup.
Cut off stalks from fennel (you may reserve some of the feathery tops for garnish) and rinse well. Halve the fennel bulbs lengthwise and cut out and discard the tough inner cores. Chop remaining fennel.
sauté fennel, butter, and onion in soup pot for 10 minutes.
Add water and lemon juice, bring to a boil, reduce heat and simmer 30 minutes.
Meanwhile, combine cream with tarragon and fennel in a small pot. Simmer on low heat to infuse the cream.
After soup has simmered 30 minutes, blend with an immersion blender to a smooth consistency. Stir in cream and serve.