Bring water to boil with orange juice, granulated sugar, honey, and cardamom and reduce to half.
Flavor with Cointreau.
Lay the orange slices flat on a tray or plate and pour the mixture over them.
Cover with plastic wrap and let marinate for 24 hours.
For the coconut soup, mix together coconut meat, simple syrup, lime juice, lemon zest, coconut liqueur, peppermint, and ice cubes until all the ice is gone.
Before serving, froth with the mixer again.
Portion the coconut soup into deep dishes.
Drain the orange slices and lay them in the soup.
Add a scoop of the prepared Mai Tai sorbet to each and garnish with peppermint.
