In a food processor, pulse yolk, mustard, and lemon juice to combine. Mix oils in a measuring cup. With motor running, add oils to yolk mixture in a slow, steady stream. Process until oils are incorporated and dressing has emulsified. Transfer dressing to a bowl and stir in pepper and 1 cup parmesan. If dressing is too thick to drizzle, stir in up to 2 tbsp. warm water. Cover and refrigerate while you prepare the rest of the salad, or up to 1 day.
Make the tuiles: Preheat oven to 350°. On a baking sheet lined with a silicone baking mat or a piece of cooking parchment, divide remaining 1 cup parmesan into 6 piles (about 2 1/2 tbsp. per pile, spaced about 2 in. apart). Using your finger, gently pat each pile into a circle with an even thickness and a diameter of about 4 in. Bake until golden brown, about 5 minutes. (Watch carefully, as cheese can burn easily.) Remove sheet from oven and let stand 1 minute, then transfer tuiles to a cooling rack or an airtight container (they'll keep for 1 day).
Divide lettuce leaves among 6 chilled salad plates. Drizzle each with a generous amount of dressing. Sprinkle with almonds and top each salad with a tuile. Serve immediately.
Note: Nutritional analysis is per serving.