Preheat a grill or griddle over medium heat and lightly apply a thin layer of cooking oil. While the griddle heats, season both sides of the chicken breasts with Italian seasoning. Place the chicken breasts on the hot griddle and cook for 4-6 minutes per side (longer for thick chicken).
While the chicken grills, cook the pasta noodles according to the package directions. Drain the pasta, reserving ½ cup of pasta water for possible use later. Set the cooked noodles aside
After the chicken cooks completely, remove it from the griddle and allow it to rest for at least 10 minutes before slicing.
While the chicken rests, make the bruschetta. In a large, deep pan heat the olive oil over low-medium heat. Add the onion, and stir for 3-5 minutes until the onions begins to heat and becomes slightly fragrant. Next, add the garlic, salt, and tomatoes. Continue to stir for 1-2 minutes, just long enough to warm the tomatoes and bring out the flavor of the garlic.
Next, add the cooked pasta, and drizzle it with the balsamic vinegar. Turn off the heat, then, add the shredded Parmesan cheese, and toss to combine the ingredients.
Divide the pasta evenly among serving dishes and top with thinly sliced chicken. Garnish with extra Parmesan cheese, balsamic vinegar or glaze, and fresh basil.