Rub the olive oil over the red peppers, then cook under a preheated hot grill for 10–15 minutes, turning occasionally, until blackened all over.
Meanwhile, cook the eggs in a saucepan of boiling water for 8 minutes. Drain, then cool under cold running water.
Transfer the peppers to a bowl, cover with clingfilm and leave until cool enough to handle. Peel away the blackened skin and discard the seeds, membranes and stalks then tear into strips.
Shell the eggs and cut into quarters.
Whisk together the vinegar and extra virgin olive oil in a bowl and season well. Toss the rocket with 1 tablespoon of the dressing. Arrange on a serving plate with the red peppers, eggs and anchovies, and drizzle over the remaining dressing. Serve immediately.