Wash, dry, top and tail the courgettes and grate coarsely into a bowl. Take up handfuls and squeeze hard over the sink to expel as much moisture as possible. Repeat until you have dealt with them all.
In a large saucepan melt the butter with the cream and over moderate heat reduce by half. Stir in the courgettes and the basil and cook, stirring two or three times, for 2 minutes. Season