1. Snap the woody ends form the asparagus spears and cut in half on the diagonal. Cook in boiling water for 1 minute. Drain, then plunge into cold water and set aside.
2. Place the mustard, lemon juice, honey, and garlic in a large saucepan and season with pepper. Bring to a boil, then reduce heat and add the mushrooms, tossing for 2 minutes. Cool.
3. Remove the mushrooms from the sauce with a slotted spoon. Return the sauce to a boil, then reduce heat and simmer for 3-5 minutes, or until reduced and syrupy. Cool slightly.
4. Toss the mushrooms, arugula, and chopped bell pepper together. Put on a plate and drizzle with the sauce.