Preheat the grill to hot and cut 450g of white bread into small cubes after removing crusts.
Toss bread cubes in a bag with 90ml olive oil, salt, and pepper until evenly coated.
Grill the bread cubes on a baking tray until evenly browned, shaking occasionally.
Cook the broad beans in boiling water for 3-4 minutes until tender.
Drain the beans, refresh in cold water, and remove them from their pods.
Slice each lettuce into six wedges and arrange on a platter with beans and cheese shavings.
Combine the mustard, vinegar, 120ml olive oil, cream, and sugar in a jar and shake well.
Pour the dressing over the salad, toss gently, and serve.