Preheat oven to 425F.
On a large baking sheet, toss asparagus with olive oil and season with salt and pepper.
On the other side of the baking sheet, toss cherry tomatoes with olive oil and season with salt and pepper. Roast for 10 minutes.
Remove from oven and sprinkle mozzarella on the asparagus. Roast 10 more minutes. If you'd like, finish under the broiler to get a char on the cheese.
Meanwhile, make balsamic glaze: Heat balsamic vinegar in a small pot over medium heat. Bring to a gentle boil, then reduce to simmer, stirring occasionally, until the vinegar thickens and is reduced (about 15 minutes). It should be thick enough to coat the back of a spoon. Remove from heat and allow to cool. Glaze will continue to Thicken as it cools.
When asparagus is done, move to a serving platter. Toss the tomatoes with the basil and top the asparagus with them. Drizzle with balsamic glaze.
