Add the blueberries, lemon juice and sugar into a small saucepan. Muddle some of the blueberries with the back of a spoon, mix and place over medium heat. Bring to a boil then simmer for about 10 minutes.
Remove from heat, crush the basil in your hands and place in the warm reduction to steep for about 5 minutes.
Strain the mixture and chill.
Add the rosé ice cubes and strained reduction to a blender and blend at high speed until smooth.
Pour into glasses and garnish with blueberries and a basil leaf.