Cut off the tops of the rolls and set the tops aside; pull out the soft bread inside the rolls, creating a cup. Finely chop the bread you removed, put it in a small bowl, and drizzle it with 2 tablespoons of the olive oil.
Peel the cucumbers in alternating strips and cut them into small chunks.
Put the tomatoes in a large bowl. Add the cucumbers, onion, and chilli and drizzle with the remaining 60 ml (¼ cup) oil. Season with the oregano and a pinch of salt and toss to combine.
Divide the salad among the four rolls and sprinkle with the chopped bread. Place the tops back on the rolls, press gently, and let them rest for 30 minutes before serving.