In a medium bowl, combined sliced strawberries and sugar. Cover with plastic wrap and let sit for 30 minutes.
Pulse strawberry-sugar mixture, chopped basil, and lime zest in a food processor or blender until berries are almost pureed.
In another bowl, whisk together Greek yogurt and heavy cream until smooth. Add strawberry mixture and stir to combine.
Pour mixture into bowl of ice cream maker and freeze according to machine manufacturer's instructions, or alternatively, pour into popsicle molds and freeze for 2-3 hours until firm.