Over medium heat bring half & half to a low boil. Turn heat down to a slow simmer and cook fennel in cream until fennel is very tender (about 20-30 minutes).
Remove from heat and cool cream mixture.
Remove cooked fennel from half & half and add to food processor with cooked artichoke bottoms.
Pulse veggies until fennel and artichokes are pureed.
Add more half & half to warm cream to make 2 cups.
In a medium mixing bowl, add puree, half & half, whipping cream, condensed milk, vanilla, anise extract and green food coloring. Mix well with whisk and pour mixture into a table top ice cream maker.
Turn ice cream maker on for 30 to 40 minutes or until ice cream is light and fluffy. Store in airtight container in freezer.
