Working one at a time, wet rice paper for 10-15 seconds and transfer to a work surface. Place lettuce, basil, mint, and cilantro in the center of each wrapper; top with carrots, cabbage, bell pepper, cucumber, and avocado; season with salt and pepper, to taste.
Bring the bottom edge of the wrap tightly over the filling and then folding in the sides, rolling from bottom to top until the top of the sheet is reached, being careful not to tear the rice paper; cover with damp paper towels. Repeat with remaining wrappers and filling.
Serve immediately with peanut sauce.
In a small bowl, whisk together peanut butter, soy sauce, lime juice, brown sugar, chili garlic sauce, and ginger. Whisk in 2-3 tablespoons water until desired consistency is reached.