- Hold a mushroom, cut side up, in your hand. Using small sharp knife, carefully scrape to remove most of dark brown “gills”. Repeat with remaining mushrooms.
- Prepare marinade in large, shallow glass dish.
- Add mushrooms and turn to coat.
- Let mushrooms marinate at least 30 minutes or up to 4 hours.
- In medium bowl, whisk together vinegar, oil and mustard to make dressing.
- Season with salt and pepper and set aside.
- Prepare hot charcoal fire or preheat gas grill on high.
- Grill mushrooms, turning often, until tender and grill-marked, about 10 minutes.
- Lightly toast rolls, if desired.
- To assemble sandwiches, spread goat cheese on both sides of rolls.
- Arrange mushrooms on bottom of each roll.
- Add arugula to dressing in bowl and toss well.
- Place arugula leaves on top of each mushroom, cover with bun tops and serve.