How to Make It
Preheat broiler to high with oven rack 4 inches from heat.
Lightly coat a large rimmed baking sheet with cooking spray. Arrange carrots, fennel, bell pepper, and cauliflower in a single layer on prepared baking sheet; drizzle with 1 tablespoon oil. Season with ¼ teaspoon each salt and pepper. Broil, stirring once halfway through, until lightly charred, 8-10 minutes.
Meanwhile, whisk together vinegar and remaining 6 tablespoons olive oil, ¾ teaspoon salt, and ½ teaspoon black pepper in a small bowl; set aside.
Remove vegetables from oven; set aside. Scoop out some crumb from bread halves to create 2 shells. Place shells on a clean rimmed baking sheet; broil until golden, about 1 minute.
Drizzle 2 tablespoons dressing over toasted bread shells. Top with roasted vegetables, then drizzle with additional 2 tablespoons dressing. Top with cheese. Broil until cheese is melted, about 1 minute. Cut into pieces, then garnish with fennel fronds.
Toss arugula with remaining dressing. Serve with sandwiches.