Combine all the ingredients for the dressing in a high speed blender and process until very smooth. Check the seasoning, and set aside.
Tear the ciabatta into roughly shaped croutons and place on a baking tray. Transfer to a 200°C (Gas Mark 6, 400°F) oven for 10 minutes or until crisp.
Heat a ridged griddle pan on a high heat and rub a small amount of olive oil on to the surfaces of the lettuce wedges. Add the lettuce to the griddle pan and leave to cook, without moving it, for 3 minutes before turning over to cook the other sides. This should allow you to create distinct char marks. When lightly char marked on all sides, remove from the pan and rest on some kitchen paper to cool slightly.
Arrange the lettuce on plates, and drizzle with the dressing. Scatter over the croutons and some dairy-free parmesan before serving.
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