In a bowl, mix together coconut milk, brown sugar, dash of salt, and vanilla extract until the sugar has dissolved. Place mixture in the fridge to cool for at least one hour. Rinse and cut off the tops of the strawberries. Smash strawberries in a separate bowl with potato masher or in a blender. Following the directions of your ice cream maker, slowly add your coconut milk mixture into the ice cream maker until it doubles in size (around 20 minutes). Add in mashed strawberries until well combined. Eat right away or freeze for later (if it lasts that long).