Remove peppers from jar. Place in bowl and drizzle with a bit of olive oil and sprinkle with salt and pepper.
To prepare the sandwiches, cut your ciabatta rolls in half and butter each piece. This will help prevent moisture from getting into the bread. Place a layer of red pepper on bottom slice of bread.
Top with a generous layer of cold meats (4 or 5 layers).
Pat your Bocconcini slices dry with a piece of paper towel. Top the cold meat with a layer of the bocconcini slices. Drizzle some balsamic vinegar over the Bocconcini slices.
Top with a generous layer of arugula. Top with the top slice of ciabatta.
Wrap each sandwich tightly with plastic wrap and place on a platter. When all the sandwiches are prepared, place the platter in the refrigerator. Place a heavy skillet on top of sandwiches to apply weight. Refrigerate at least 6 hours or ideally, overnight. When ready to serve, remove from plastic wrap.
For a cute presentation or picnic you can trim the sides and wrap each in parchment paper tied with string.