Bring large pot of water to boil and cook pasta according to package directions until al dente.
In a small bowl, combine garlic, grill seasoning, hot sauce, Worcestershire sauce, and 2 tablespoons of th vinegar and mix.
Whisk in 1/4 cup olive oil and divide the mixture into 2 bowls.
Add the sliced onion to one and the chicken to the other. Toss to coat both thoroughly and marinate for a few minutes.
In a salad bowl, combine mustard and remaining 2 tablespoons vinegar with a little salt and pepper.
Whisk in the remaining olive oil and then add the grated cheese.
Once pasta is cooked and drained, add it to the salad bowl and toss to coat.
Grill the onion slices until well marked, about 2-3 minutes.
Grill the chicken for 3 to 4 minutes on each side.
Remove both onion and chicken from grill to cutting board and allow to cool for a few minutes.
Coarsely chop the onions and cut the chicken into slices.
Add them to the pasta.
Add the arugula, radicchio, basil, parsley, celery, mozzarella and tomato; toss thoroughly.
Season with salt and pepper to taste.
** We aren't big fans of arugula and radicchio, so we use romaine and iceberg lettuce. we've also kept the chicken, pasta and onion separate from the salad and had as 2 dishes - Ijust make a little extra dressing.