Special equipment: 12 (10-inch-long) pieces of kitchen string
Position a rack in the center of the oven and preheat the oven to 450 degrees F. Spray a heavy baking sheet with vegetable oil cooking spray. Set aside.
For the dressing: In a small bowl, whisk the red wine vinegar, oregano, fennel seed, mustard, salt, pepper and garlic. Gradually whisk in the oil.
For the chicken: In a medium bowl, combine the salami, pepperoncini, prosciutto, provolone and tomatoes with 1/4 cup of the dressing; toss to blend evenly.
Place the chicken breasts, smooth-side down on the work surface with the thickest part at the top and the straight side on the left. Using a very sharp knife and starting on the right side, cut each chicken breast almost in half horizontally (stopping close to the left side), creating a pocket for stuffing. Open the chicken breasts like a book.
Mound a fourth of the stuffing onto the right side of the breast, and press firmly to compact. Fold the left side (flap) of the chicken tightly over the stuffing. Lay three 10-inch pieces of string on the work surface 1 to 11/2 inches apart. Place the chicken on the strings and tie the strings around the chicken at intervals to keep the flap closed over the stuffing. Press in any stuffing pieces that fall out.
Place the chicken breasts on the prepared baking sheet. Drizzle with 1/4 cup of the dressing.
Roast until the chicken is cooked through, 18 to 20 minutes. Using tongs, transfer the chicken to a sheet of foil. Let rest 5 minutes.
For serving: Divide the arugula among four plates. Cut the strings off the chicken. Cut each breast on a slight diagonal into 1/2-inch-wide slices. Fan the slices of one breast over the arugula on each plate. Drizzle with the dressing and serve.