Preheat the oven to 200C/400F/Gas 6.
Place the peppers in a roasting tin and toss in olive oil, then season. Roast until lightly blackened and tender, 20-30 minutes.
Roll out the puff pastry on a lightly floured surface and cut in half to form two rough squares. Score a rim about 1cm lightly from the edge. Place the puff pastry squares on a greaseproof paper-lined baking sheet, prick all over with a fork, except the rims.
Bake in the oven for 5-7 minutes or until the rims are lightly puffed up. Remove from the oven and leave to cool slightly.
Either scatter the chopped anchovy or spread a little pesto over the base, then layer on the roasted peppers. Slice the cheese and arrange evenly over the peppers. Paint a little egg wash on the pastry rims. Return to the oven and bake until golden for about 15 minutes.