- Drain roasted peppers in strainer set over small bowl, reserving liquid. You should have about 2 tablespoons liquid. Thinly slice peppers and set aside.
- Whisk vinegar, oil, mustard and 1 tablespoon water into red pepper liquid in bowl to make dressing.
- In medium bowl, place 1 tablespoon dressing and reserve.
- Prepare grill or heat grill pan over medium-high heat.
- Brush remaining dressing over both sides of mushrooms.
- On grill or pan, place mushrooms cut side down. Cook until tender, turning once, 3 to 4 minutes per side.
- Place 1 mushroom on bottom of each bun. Top with pepper slices.
- Add arugula to reserved dressing in bowl and toss well.
- Place some arugula salad on top of each mushroom, cover with bun tops and serve.