Add chopped strawberries to a pan over medium heat with 2 tbsp sugar and bring to a simmer, stirring frequently until you have a jammy sauce like consistency (about 10 mins), set aside to cool down.
Add double cream and condensed milk to the bowl of a stand mixer (or a mixing bowl if using a whisk or beater). Beat on medium until whipped cream consistency.
Gently fold through all but 2 tbsp of the strawberry mixture, lime zest and lime juice and transfer to a loaf tin or container with a lid.
Swirl the remaining strawberry mixture over the top.
Cover and set in freezer for at least 5 hours.
Serve with fresh strawberries!
