Heat oven to 200C/fan 180C/gas 6. Tear the gluten free bread into big, ragged croutons or, if you prefer, cut with a bread knife.
Spread over a large baking sheet or tray and sprinkle over 2 tbsp olive oil.
Rub the oil into the bread and season with a little salt if you like (sea salt crystals are best for this). Bake for 8-10 mins, turning the croutons a few times during cooking so they brown evenly.
Rub chicken breasts with remaining oil, season. Place pan over a medium heat for 1 min, until hot, but not smoking. Lay the chicken on the pan (it will sizzle if it’s hot enough) and leave for 4 mins.
Turn the chicken, then cook for 4 mins more. Check if it’s cooked by poking the tip of a sharp knife into the thickest part; there should be no sign of pink and juices will run clear.
Mash the anchovies with a fork against the side of a small bowl. Grate a handful of cheese and mix with the rest of the dressing ingredients. Season to taste. It should be the consistency of yogurt – if yours is thicker, stir in a few tsps water to thin it.
Shave the cheese with a peeler. Tear lettuce into large pieces and put in a large bowl. Pull chicken into bite-size strips and scatter half over the leaves, along with half the gluten free croutons. Add most of the dressing and toss with your fingers. Scatter the rest of the chicken and croutons, then drizzle with the remaining dressing. Sprinkle the Parmesan on top and serve straight away.