Preheat the oven to 425°F (220°C). Arrange the trimmed asparagus spears on a large baking sheet. Drizzle them with extra-virgin olive oil and season generously with kosher salt and freshly ground black pepper. Add a pinch of Italian seasoning for an herbaceous touch. Gently toss to coat the asparagus evenly, then shift them to one side of the pan. Sprinkle the shredded mozzarella over the asparagus in a generous layer.
On the opposite side of the baking sheet, spread the halved cherry tomatoes. Drizzle them with a bit more olive oil and season with salt and pepper. Roast everything in the preheated oven for about 20 minutes, or until the asparagus becomes tender and the cheese melts into a bubbly, golden layer.
While the vegetables roast, prepare the balsamic glaze. In a small saucepan set over medium heat, combine the balsamic vinegar and honey. Let the mixture simmer gently, stirring occasionally, until it reduces by half—about 15 minutes. The glaze is ready when it thickly coats the back of a spoon. Remove from heat and allow it to cool slightly.
Once the asparagus is roasted and the cheese has melted to perfection, carefully transfer the asparagus to a serving platter. Spoon the roasted cherry tomatoes over the top, then drizzle everything generously with the warm balsamic glaze. Finish with a scattering of fresh basil ribbons for a vibrant burst of color and flavor.