Place the strawberries and 1/4 cup of the sweetener in a high-speed blender and process a few times until almost pureed. Add the cream cheese and blend until thoroughly combined then add the coconut cream (and vodka, if using) and blend until creamy.

Meanwhile, add the heavy whipping cream and the remainder of the sweetener to a large chilled bowl and whip until stiff peaks form. Fold into the blended coconut milk mixture until just combined.

Scrape the ice cream into a freezer container. Place container in the freezer and give the ice cream a good stirring every 30 minutes for the first 2-3 hours, then every hour for the next 2 hours.

Allow ice cream to sit out at room temperature for about 15 minutes to thaw out slightly before scooping.