1. Heat the coconut milk over very low heat in a small non-stick saucepan.
2. Add the white chocolate pieces, a little at a time. Make sure the mixture is smooth and homogeneous. Remove the saucepan from the heat, let it cool, then refrigerate for at least 2 hours.
3. In a saucepan, add the strawberries and sugar. Let it cook over low heat for 10 minutes, covered.
4. Remove the mixture from the refrigerator and whip it with an electric mixer.
5. Divide half of the mousse into small cups, place a spoonful of strawberry compote in the center, top with the rest of the mousse and refrigerate.
6. Serve chilled.