Trim the fennel by cutting off the root end and the fronds. Remove outer layer of bulb and discard. Dice bulb. Set aside.
Chop fronds with the parsley until you have a moist, fine puree. (I use a small food processor) Squeeze this puree in a paper towel over a bowl to extract juice. Save juice. Discard solids.
In a small heavy saucepan, melt butter over medium heat and cook shallots until soft, but not brown. Add diced fennel, cover the pan, and cook gently for 8 minutes. Deglaze pan with wine and cook until slightly reduced.
Add the cream, bring to a boil and season with salt. Allow to boil for a few minutes until sauce is smooth. Add the reserved fennel and parsley juice. The sauce will turn a light green color.