Prepare an ice-water bath. Whisk yolks and sugar in a large metal bowl. Set over a large pot of simmering water, and slowly whisk in Midori. Continue to whisk until thick and doubled in volume, about 6 minutes. Set bowl in ice-water bath, and let cool, stirring occasionally, for 10 minutes.
Whisk the cream in a medium bowl until soft peaks form. Whisk in creme fraiche and lime zest. Gently stir cream mixture into yolk mixture. Use immediately (or cover, and refrigerate for up to 2 hours).
The egg yolks in this recipe are not cooked. This dish should not be prepared for pregnant women, babies and other young children, the elderly, or anyone whose health is compromised.
Other spirits, such as amaretto or rum, may be substituted for the Midori, but the gorgeous chartreuse green of this sauce complements the colors of the pineapple mousse and pistachios.