Peel the onion and finelh chop. Squeeze juice from the lemon. In a bowl, whisk together 2 tablespoons lemon juice, the onion, honey, and olive oil and season with salt and pepper. Set aside.
Rinse the peppers, wipe dry, cut into quarters and remove seeds. Place peppers with skin side up on a baking sheet.
Roast the peppers under preheated oven grill or boiler until the skin is blackened and blistered. Remove from oven. Cover with a damp kitchen towel and let stand for 10 minutes. Remove the peel and mix peppers with the onion mixture. Season with salt and pepper and let marinate for 30 minutes.
Rinse the arugula and spin dry. Remove any tough stems. Tear or cut into bite-sized pieces, if desired. Mix with pepper quarters just before serving.