Instructions

• In a small bowl combine the aioli ingredients, including 1 teaspoon salt. Refrigerate until ready to assemble the sandwiches.
• In a small bowl whisk the marinade ingredients, including 1 teaspoon salt and ½ teaspoon pepper. Place the mushroom caps, gill sides down, in a large glass baking dish. Brush the mushroom caps generously with the marinade and turn the caps over. Spoon the rest of the marinade over the gill side. Allow the mushrooms to marinate at room temperature for 15 to 20 minutes.
• Prepare the grill for direct cooking over medium heat (350° to 400°F).
  Prepare the grill for cooking over medium heat (400°F).
• Remove the mushrooms from the dish and reserve the marinade. Lightly season the mushrooms with salt and pepper. Brush the cooking grates clean. Grill the mushrooms, gill side down, over direct medium heat, with the lid closed, until they begin to soften, 4 to 6 minutes. Brush the cap sides of the mushrooms with some of the remaining marinade from the dish. Turn the mushrooms over and continue grilling until tender when pierced with a knife, 4 to 6 minutes more. During the last 30 seconds to 1 minute of grilling time, toast the rolls, cut side down, over direct heat.
  Remove the mushrooms from the dish and reserve the marinade. Lightly season the mushrooms with salt and pepper. Brush the cooking grates clean. Grill the mushrooms, gill side down, over direct medium heat, with the lid closed, until they begin to soften, 4 to 6 minutes. Brush the cap sides of the mushrooms with some of the remaining marinade from the dish. Turn the mushrooms over and continue grilling until tender when pierced with a knife, 4 to 6 minutes more. During the last 30 seconds to 1 minute of grilling time, toast the rolls, cut side down, over direct medium heat.
  Remove the mushrooms from the dish and reserve the marinade. Lightly season the mushrooms with salt and pepper. Brush the cooking grates clean. Grill the mushrooms, gill side down, over medium heat, with the lid closed, until they begin to soften, 4 to 6 minutes. Brush the cap sides of the mushrooms with some of the remaining marinade from the dish. Turn the mushrooms over and continue grilling until tender when pierced with a knife, 4 to 6 minutes more. During the last 30 seconds to 1 minute of grilling time, toast the rolls, cut side down, over medium heat.
• Spread aioli on the toasted rolls and top each one with some arugula and a mushroom. Serve warm.