Preheat the grill. Arrange the red and yellow peppers on a grill rack and cook for 20-30 minutes until well charred and blistered, turning regularly. Transfer to a large bowl and cover with clingfilm. Leave the peppers to cool completely, then peel, using a bowl underneath to catch all of the juices. Slice the flesh into strips, discarding the seeds and cores. Place in a bowl and set aside until needed.
Place the extra-virgin olive oil in a small bowl and whisk in the balsamic vinegar, then season with a pinch of salt and plenty of pepper. Arrange the roasted pepper strips on a platter or individual plates and drizzle over the dressing. Arrange the anchovies in a criss-cross pattern and scatter over the olives. Roughly tear up the basil leaves and use as a garnish. Serve at room temperature.