Have ready a large bowl of ice water.
Bring broth to boil in a large pot. Add asparagus; cook until crisp tender, about 2-3 minutes. Using tongs, transfer asparagus to bowl of ice water. Reserve 1 cup broth in a small bowl. Drain asparagus, pat dry. (Can be made 1 day ahead. Wrap asparagus in paper towels. Seal in plastic bag. Cover broth. Refrigerate asparagus and broth until ready to use.)
Heat 1 tablespoon oil in medium nonstick skillet over medium heat. Add 1 cup of chopped green onions, shallots, and sugar. Saute until onions and shallots are tender, about 5 minutes. Add garlic, saute 1-2 minutes longer Stir in reserved 1 cup of broth, mustard, lemon juice, thyme and lemon peel. Simmer until slightly thickened and liquid is reduced to 1-1/4 cups, about 5 minutes. Season with salt and pepper. Cool to room temperature.
Arrange asparagus on platter or individual plates. Spoon sauce over. Sprinkle with remaining green onions and bell peppers.
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