Preheat your oven to 425 degrees F. Line a large baking sheet with foil and set aside.
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, about 8-10 minutes. Drain (reserving 1/4 cup of water) and set aside.
Meanwhile, heat 1 tbsp of olive oil in a large pan over medium-high heat. Season the chicken all over with 1 tbsp Italian season, salt, and black pepper (using more Italian seasoning if needed). Brown the chicken for 2-3 minutes one each side, and then transfer the chicken to the prepared baking sheet. Add half of the parmesan and mozzarella cheese on top of the chicken. Bake the chicken for 10-15 minutes or until cooked through. The cheese should be brown and bubbly by this point. Remove from heat and set aside.
While the chicken is baking and the pasta is boiling, prepare the bruschetta and sauce. In the same pan that you cooked the chicken, heat the remaining olive oil over medium heat. Add the tomato and remaining Italian seasoning. Cook for 2 minutes, and then add the balsamic vinegar, sugar, and a dash of salt and black pepper. Cook for another minute until slightly reduced. Remove the pan from heat and stir in the basil, parsley, and chives. Stir in 2 tbsp of unsalted butter until melted. Set the pan aside.
Once the pasta has cooked and you have drained the water (reserving 1/4 cup of pasta water), add the pasta back to the pan. Over low heat, add the remaining 2 tbsp of butter, reserved pasta water, garlic, and a dash of salt and black pepper.
To assemble, divide the pasta among four plates or bowls. Sliced the chicken and divide among the four plates. Top each plate with bruschetta and sauce and garnish with the remaining cheeses and parsley. Enjoy immediately!