Cook pasta according to package instructions—aim to have the texture slightly undercooked.
Whisk together all of the vinaigrette ingredients and set aside. This can also be made a day in advance. Taste for salt.
In a large mixing bowl, combine the cooked pasta, bell pepper, basil, cherry tomatoes, olives, mozzarella, salami, and radicchio. Pour over the dressing and stir once more to combine.
Return pasta salad to refrigerator and chill until ready to serve.
For picnic salad in jars, fill the jars with about 1/3 cup of arugula, pasta salad, and then seal with the lid. Chill until ready to serve.