Preheat the oven to 375°F.
Cook the noodles according to the package instructions.
While the noodles cook, add 1 tablespoon of olive oil to a large skillet on the stovetop over medium heat.
Once the pan is hot, add the chicken breasts to it and sear for 4-5 minutes on each side, until the chicken is cooked through. Pull the chicken out of the pan and chop it into 1-inch pieces.
Add the cooked noodles to a 9x13 inch, or other 3-quart, baking dish. Add one tablespoon of olive oil, salt, and pepper to the noodles and toss to combine.
Spread the cubed chicken breast over the noodles, drizzle 2 of the tablespoons of the balsamic vinegar over the chicken, then top with the cherry tomatoes and mozzarella.
Bake the casserole for 30 minutes, until the cheese is browned on top.
Meanwhile, make the Italian Salad: in a small bowl, whisk together the olive oil, vinegar, honey, salt, and pepper. Put the lettuce, tomatoes, onion, and carrots in a large bowl. Pour the dressing over the salad and toss to combine.
Once the casserole comes out of the oven, drizzle with the remaining 2 tablespoons of balsamic vinegar, then sprinkle the basil over top. Serve with the Italian salad.