Preheat your oven to 400°F (200°C). Prepare a baking sheet with parchment paper.
Arrange the asparagus in a single layer on a baking sheet, drizzle with the olive oil, and sprinkle with the salt and pepper.
Roast for 15-20 minutes, or until tender and slightly charred.
Meanwhile, place the cherry tomatoes in a small baking dish. Drizzle with a little olive oil, season with salt and pepper, and roast in the oven until they are blistered and starting to burst, about 10-15 minutes.
Remove the asparagus from the oven and scatter the sliced fresh mozzarella and blistered cherry tomatoes over the top. Return to the oven and bake just until the mozzarella is melted, about 3-5 minutes.
Transfer the asparagus to a serving platter.
Drizzle the balsamic glaze all over the asparagus, melted mozzarella, and tomatoes. Sprinkle with fresh basil leaves. If desired, finish with a drizzle of extra virgin olive oil.
Serve the oven-melted Caprese asparagus warm. Enjoy!