To roast the red peppers: Set your oven to the Broil setting. Slice the sides off the red peppers and place skin side up on a baking sheet (*I like to trim the ends so they lie as flat as possible, as they will brown better than pieces that are sloped). Place under the broiler until very well charred (blacon top, about 10 minutes (watch closely after 5 minutes. You'll want them to be mostly blackened on top.) Remove from the oven and immediately place the peppers in a plastic ziploc bag. Pop in the refrigerator for 30-40 minutes. Remove peppers from bag and peel off the blackened skin with a knife. Discard the skin and slice the peppers in to strips. Place in a bowl and drizzle with a bit of olive oil and sprinkle with salt and pepper. Set aside.
To prepare the sandwiches: Cut your ciabatta in half and butter each piece (or you could brush with a bit of olive oil, if you prefer, but butter will help prevent moisture from getting into the bread. Place a generous layer of cold meats (4-5 over-lapping layers). Top with cooled roasted red pepper strips. Take your Bocconcini slices and place on a piece of paper towel. Top with another piece of paper towel and pat to dry a bit. Top the red peppers with a layer of the Bocconcini slices. Drizzle some balsamic vinegar over the Bocconcini slices and sprinkle with salt and pepper. Top with a generous layer of arugula. Top with top slice of ciabatta.
Be sure to read the "Cook's Notes" in the original post, for more tips, options, substitutions and variations for this recipe!