Stir the ingredients for the dipping sauce together in a small bowl.

Toss the herbs and lettuce in a bowl until evenly combined. Fill a shallow bowl with warm tap water and drop in 4 of the rice papers, one at a time. In about 3 minutes they should be very soft and pliable. Lift them from the water and lay them out on a clean kitchen towel. Divide one third of the herb mixture among the 4 papers, arranging each portion in a strip lengthwise across the center. Sprinkle with peanuts. Roll each one up into a snug cylinder and place it on a platter. Repeat the soaking, filling, and rolling in two more batches. Serve the rolls right away with the dipping sauce or cover them with a damp paper towel and then plastic wrap; they’ll hold for about 2 hours in a cool spot (not the refrigerator).