Preheat the oven at 200℃. Chop the strawberries and place into a baking dish. Add the sugar, vanilla and balsamic vinegar. Place in the oven and bake for 30- 40 mins, until jam like. Set aside to cool.
Meanwhile, add the basil and lime juice to a blender jar and blend until basil is fully chopped.
In a saucepan, heat the double cream and milk until simmering. Allow to cool.
In a large mixing bowl, mix everything together. Pour into your chosen container and freeze overnight. Use your ice cream maker to churn and serve.