Wash the basil, dab dry and, except for a few leaves for garnishing, pluck the basil. Roast pine nuts in a pan without fat until golden brown. Set aside about 1/3 for sprinkling. Grate the Parmesan finely.
Mix basil, pine nuts, parmesan and 3 tablespoons of oil in a universal chopper. Season to taste with salt. Peel the white asparagus. Wash the green asparagus. Cut off woody asparagus ends. Cut the asparagus thinly on a slicer or bread machine.
Blanch in salt water for about 10 seconds. Rinse asparagus in cold water and then drain. Pluck the rocket, wash and drain. Heat the grill or normal pan and fry the baguette slices in it until light brown.
Remove and set aside. Wash, clean and halve the cherry tomatoes. Season lemon juice with salt and pepper. Beat the remaining oil into it. Mix asparagus, rocket salad and tomatoes with the vinaigrette.
Arrange asparagus salad on plates. Sprinkle with pine nuts. Arrange one baguette slice on each plate. Put pesto on the baguette slices and drizzle on the salad. Cut dried tomatoes into small pieces and sprinkle on the salad.
Garnish with basil.