White asparagus: Peel the stems with a vegetable peeler from top to bottom, starting below the tips. Remove any woody ends with a knife and cut the asparagus into 5cm pieces.
Green asparagus: Peel only the bottom third. Remove any woody ends with a knife and cut the asparagus into 5cm pieces.
In a large pot, bring salted water with sugar and butter to the boil; reduce heat and simmer gently until asparagus is tender and can be easily pierced with a sharp knife, about 20 to 25 minutes. The cooking time varies depending on the thickness of the asparagus. Remove the asparagus with a slotted spoon and cook the broccoli in the same water until cooked but still al dente, about 6 to 8 minutes. Drain.
Toast the hazelnuts in a dry frying pan, turning them often, until they start to smell nutty. Place the nuts in a colander and rub them against each other between your palms to remove the skins. Chop and set aside.
For the dressing; stir vinegar, salt and pepper in a small bowl. Add the oil in a steady stream. Add egg yolks and whisk until smooth and thick.
Layer asparagus, broccoli, nuts and parsley in a glass bowl and pour the dressing on top. For best results, chill the salad for 1 hour before serving.