Prepare the Spicy Garlic Aioli. Combine mayonnaise, lemon juice, 1 teaspoon garlic, 1/4 teaspoon salt, 1/8 teaspoon pepper and the cayenne pepper in a small bowl. Cover and refrigerate until ready to use.
Clean the mushroom caps. Wipe away any dirt and cut off remaining stems. Remove the gills by scraping them off with a spoon.
Whisk Balsamic dressing, soy sauce and garlic together in a small bowl. Place prepared mushroom caps in a shallow dish and pour marinade over the top. Let the Portobello Mushrooms marinate at room temperature 30 minutes.
Spray cold grate of grill with grilling spray. Preheat grill to medium heat. Grill the Portobello Mushrooms about 4 minutes on each side until just tender.
Butter and toast buns while the Portobello Mushrooms are cooking.
Spread aioli as desired on each top bun. Place a grilled Portobello Mushrooms on each bottom bun and top with arugula and top bun. Serve immediately.