In a large pot add mussels, shallots, sparkling wine, garlic and butter. Cover and place over medium heat. Steam mussels until shells are opened.
In stainless steel bowl add egg yolks and sparkling wine. Place over bain marie. Whisk until it doubles or triples in volume. Remove from heat. Keep warm.
Remove mussels and place in bowls. Add two tablespoons of nectar to sabayon and whisk until incorporated. Add basil to sauce and spoon over mussels. Serve immediately.