Place cream in a heavy-bottomed saucepan and heat on medium until small bubbles appear around edges.
Remove from heat once bubbles appear and stir in sugar until dissolved.
Transfer to medium bowl and allow to cool. Set aside.
Combine avocado and cream cheese in a food processor and blend until velvety smooth.
Add lime juice to avocado and cream cheese mixture and process until smooth.
Add avocado mixture into the cooled cream mixture in the medium bowl.
Fill your ice cream mixture with all the ingredients from the medium bowl. Freeze according to the manufacturer’s instructions for making soft ice cream.
Once semi-frozen, spoon this ice cream mixture into a prepared pie crust and smooth surface with a spatula.
Freeze until solid, at least 2 hours. Allow cheesecake to sit at room temperature for 10-15 minutes prior to serving to allow cheesecake be soft enough to cut.