Heat a griddle pan over high heat until it starts smoking.
Drizzle sourdough bread with oil and rub with a garlic clove.
Griddle the bread for 40 seconds per side until toasted and charred.
Cool the bread slightly and tear it into bite-sized croutons.
Blend egg yolk, anchovies, reserved oil, garlic, lemon, mustard, parmesan, and pepper into a paste.
Gradually trickle in the remaining olive oil while blending until incorporated.
Add 30ml of warm water if the dressing requires thinning.
Combine lettuce with dressing in a bowl and toss to coat.
Top with croutons and extra parmesan cheese before serving.