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 thorougly combined then add the coconut cream (and vodka, if using) and blend until creamy.
Meanwhile, add the heavy whipping cream (or another can of coconut 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. (If you have an ice cream maker - you can add the mixture to your ice cream maker and churn until smooth before adding 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 (to avoid getting too icy - skip if ice cream maker was used) then every hour or so for the next 2 hours.
Allow ice cream to sit out at room temperature for about 15 minutes to thaw out slightly before scooping.
Be sure to use full-fat canned coconut milk, not lite or coconut milk beverage.
*If your ice cream is too hard to scoop, let it sit on the counter for about 15 minutes to soften. Adding vodka to the ice cream helps to offset some of the iciness.
Please note that nutrition facts were estimated for 1/3 cup. serving.