In a small bowl whisk everything together until emulsified and set aside.
In a medium bowl, add about 2 tablespoons of the vinaigrette to the tuna and a little salt and pepper. Flake gently with a fork and set aside.
Begin by slicing the ciabatta in half lengthwise. Drizzle the 1 tbsp of olive oil over both halves. Then drizzle about a tbsp of the vinaigrette over the two halves.
Begin assembling on the bottom layer. Arrange about half of the basil leaves over the bread, followed by about half the cucumber, then the tuna, sliced olives, tomatoes, bell pepper and drizzle the rest of the vinaigrette. Then add the pickled onions, capers, pepperoncini, the rest of the cucumber and the rest of the basil leaves.
Place the top half of the bread on the sandwich and wrap tightly with plastic wrap and then with foil. Weight down the sandwich with something heavy like a skillet, books, or whatever you've got. (The NYTimes recipe suggests using your small child to sit on it but my small child was busy at the time.) Weight it down for 7 minutes, flip the sandwich over and do it for another 7 minutes.
Then store the sandwich in the fridge for at least 2 hours or overnight for best results and up to 24 hours. Slice in wedges and enjoy. (If only letting it sit for a couple hours, it can stay at room temp.)
*Try adding some arugula, sliced radish, sliced green bell peppers or sliced hard-boiled egg if you'd like.
*If you're using a different crusty bread besides a ciabatta, it's recommended to tear out some of the soft bread in the middle, after slicing the loaf, to make sort of a well for everything.
*The order in which I did this made sense to me, for keeping the bread at optimum texture, but you can assemble it however you'd like.
*While I think traditionally this is made with tuna packed in oil, I find it doesn't make a difference and tuna in water, drained well, works great too.