To make sauce, place all ingredients in a small bowl. Add ¼ cup cold water. Whisk with a fork until well combined.
Place vermicelli in a heatproof bowl. Cover with boiling water. Stand 3 minutes. Drain. Rinse under cold water. Drain again. Roughly cut into shorter lengths with kitchen scissors.
Cut tofu into 16 strips, about 1cm wide. Pat dry with paper towel. Heat 1 teaspoon oil in a medium, non-stick frying pan over a medium heat. Add half the tofu strips. Cook for 5-6 minutes, turning once, until golden on both sides. Transfer to a baking paper-lined tray. Repeat step with remaining oil and tofu. Sprinkle with sesame seeds.
Immerse 1 rice paper wrapper in a large, shallow dish of warm water for about 10 seconds. Place on a board lined with a clean, dry tea towel. Spread 1 teaspoon of prepared sauce in centre. Top with a lettuce leaf, tofu strip and a small amount of vermicelli, carrot, cucumber, shallots and mint. Roll up, folding in sides, to enclose filling. Transfer to a plastic-wrap lined tray. Repeat with remaining ingredients to make 16 rolls altogether.
Serve rolls with remaining sauce.

TIPS: To toast sesame seeds, stir in a small, dry frying pan over a medium heat until golden. Replace mint with coriander if preferred. Take care to briefly dip rice paper in water. Over-soaking makes rice paper difficult to handle. Rolls can be made up to 4 hours ahead. Line a large container with plastic wrap. Splash wrap with a little cold water. Arrange rolls in a single layer in prepared container. Cover with lid. Refrigerate until ready to serve.