Slice the bread lengthwise and open it up like a book. Brush the bottom halves of the bread with some of the vinaigrette. Layer half of the provolone over the bottom half of both sandwiches. Layer on the ham, salami, and prosciutto, folding the sliced meats to build volume into the sandwiches. Top with the peppers, lettuce, tomatoes, and oregano.
Drizzle with the remaining vinaigrette and then top with the other half of the provolone and the bread. Wrap the sandwiches in wax paper or foil. To serve, unwrap and slice them into quarters on a diagonal.
Tip: Prepping for a tailgate party or picnic? Complete the directions through step 1, top the sandwiches with the remaining provolone, wrap them in wax paper or foil, and chill them for up to 4 hours. Just before serving, lift up the top layer of bread and cheese and drizzle the remaining vinaigrette over each sub; then re-close the subs and slice them on a diagonal.