Peel asparagus and simmer in water with 1 teaspoon salt and 1 teaspoon sugar for about 25 minutes. Drain and let cool to room temperature. Rinse tomatoes, quarter, core and finely dice. Drain artichokes and slice.
Whisk together both vinegars, broth, oil and parsley. Season with salt and sugar.
Arrange asparagus, tomatoes and artichokes on plates or platters and drizzle with vinaigrette. Serve garnished with parsley.