In a large bowl, mix together honey, yogurt, lime juice and strawberries.
Working in small batches, add the mixture to a food processor or blender.
Process until creamy, about 5 minutes.
If needed, add a little water.
Serve immediately or transfer it to an airtight container and store in the freezer for up to 3 weeks.
Garnish with blackberries and whipped cream if desired.