Using a vegetable peeler, carefully shave the asparagus into a large bowl. Sprinkle in the shallots.
In a medium bowl, combine the olive oil and grapefruit juice and whisk to emulsify. Season with salt and pepper.
Pour the dressing over the asparagus and toss well. Arrange the salad on a serving plate and garnish with the quail eggs, shaved Parmigiano-Reggiano and freshly ground black pepper.