Preheat the oven to 220C/200C Fan/Gas 7. Put the red peppers on a baking tray and roast for 25–30 minutes until charred, turning them halfway through. Transfer to a bowl, cover and leave to steam until cool.
Peel off the charred skin, cut each pepper in half and scoop out the seeds. Trim off the stalks and discard. Slice the pepper flesh into 5mm/¼in-wide strips and place in a clean bowl. Season with salt and pepper.
Mix the parsley, garlic and olive oil in a small bowl and season with salt and pepper. When ready to serve, make a nest of red pepper strips on each plate and top with a hard-boiled egg.
Place three anchovy fillets over each egg and dot the plate with a little of the parsley mixture. Finally, add a few matchsticks of padrón pepper or some chilli flakes, if using, and basil leaves.