Leave the tin of coconut milk in the fridge overnight.
The next day, open the tin without shaking it - the coconut milk should have separated into a thick white cream, with a runny liquid underneath. Carefully scoop the thick white layer (probably about the top 1/3 of the tin) into a bowl, and whisk it for several minutes until it is thick and frothy. Add the icing sugar, and mix well.
Heat the oven to 200°C (Gas Mark 6 / 400°F).
Cut the strawberries into quarters (or halves if they’re quite small), and toss them in 1tbsp of balsamic vinegar. Spread them out in a single layer on a baking tray, and roast for around 10 minutes, until soft but still holding their shape.
While the strawberries are roasting, add the extra 2tbsp of balsamic vinegar to a small saucepan, and bring to the boil. Cook for a few minutes, until the vinegar has halved in volume, and is thick and syrupy.
Serve the roasted strawberries with the whipped coconut cream and the balsamic reduction.