Boil salted water in a large pot and add the barley. Once boiling again, reduce heat to medium and simmer for 25 minutes. Drain and spread the barley on a parchment-lined sheet pan to cool.
In a skillet over medium heat, toast the walnuts for about a minute until golden, then season with salt and transfer to a plate.
Add 1 tablespoon of olive oil to the skillet and sauté the diced fennel for 5 minutes. Lower the heat, season with salt, and cook for another 3 minutes until tender.
In a large bowl, combine the cooled barley, walnuts, fennel, arugula, fresh mozzarella, olives, artichokes, soppressata, pepperoncini.
Remove the sun-dried tomatoes from the oil. Roughly chop.
In a mixing jar or bowl, mix together the chopped tomatoes, 1/4 cup of oil from the sun-dried tomato jar (if there isn't enough, sub with olive oil), lemon juice and zest, honey, red pepper flakes, and oregano. Shake or whisk until well combined.
Pour half the vinaigrette over the salad and toss. Serve the salad with the remaining vinaigrette on the side so you can dress your salad as you like.