Poach the chicken breasts in a saucepan for 15–20 minutes. At the same time bring a pan of water to the boil, then add some salt and the potatoes and cook for 15 minutes.
Drain the chicken and the potatoes and leave aside to cool.Wash and dry the lettuce and line a large bowl or platter with it.
Heat the oil in a frying pan until very hot. Fry the bread a few cubes at a time until golden brown. Drain on a little kitchen paper. Slice the chicken and potatoes and place in a bowl. (If the potatoes are very small you could leave them whole or just cut in half).
Pour over the dressing and toss well. Taste and season if necessary. Spoon this mix on top of the platter of lettuce, sprinkle the croutons and parmesan shavings on top.