For the vinaigrette: Whisk the vinegar, mustard, chile paste, Italian seasoning, shallot and 1/4 teaspoon salt together in a small bowl. Gradually whisk in the olive oil. Pour into a cruet and shake.
For the salad: Combine the radishes, celery, romaine, iceberg, provolone, salami, tomatoes, pepperoncini and cherry peppers in a large salad bowl. Toss with the vinaigrette and serve immediately.