Bring the chicken broth to a boil in a large pot.
Add in the asparagus; cook until just crisp-tender (about 4 minutes).
Uning large tongs remove the asparagus to a bowl of ice water (reserve 1 cup of the chicken broth).
Drain the asparagus and pat very dry with paper towels.
Heat 3 tablespoons oil in a skillet over medium heat.
Add in the chopped green onions, shallots and sugar; saute until the onions and shallots are tender (about 5 minutes).
Add in garlic; saute 2 minutes.
Add in the reserved 1 cup broth, 1 tablespoons oil, Dijon mustard, lemon juice, thyme and lemon peel; simmer until slightly thickened and the liquid is reduced to about 1-1/4 cups (about 5 minutes).
Season with salt and pepper.
Cool to room temperature.
Arrange the asparagus on a platter.
Spoon the prepared lemon sauce over, then sprinkle with more chopped green onions.
