Roasting the asparagus alone first keeps it from steaming under the cheese and tomatoes, which only go on for the last couple of minutes under the broiler.
Preheat oven to 400°F. Line a rimmed baking sheet with foil and lightly coat with nonstick spray.
Toss the asparagus with two-thirds of the oil; arrange in a single layer on the prepared pan. Season with salt and pepper. Roast 10 minutes, until crisp-tender. Remove from the oven and preheat the broiler.
Meanwhile, toss the cherry tomatoes with the remaining oil and half the cheese in an oven-safe bowl.
Transfer the asparagus to a baking dish. Top with the remaining cheese, then the tomato mixture. Broil 5 to 6 inches from the heat for 1 to 2 minutes, until the cheese is slightly melted. Drizzle with balsamic glaze and garnish with basil, if desired.
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