Snap off the tough ends of the asparagus. Using a vegetable peeler and starting from the bottom end of the asparagus, shave upwards to create thin ribbons. Place all the ribbons in a large serving bowl.
Slice the cucumber lengthways and cut into bite-size pieces. Cut the tomatoes in half and coarsely chop the parsley. Add these to the bowl.
Place the dressing ingredients in a blender and blitz until creamy. Add a dash of oil or water if necessary. Dress and toss the salad so it's evenly coated.