Summer Vegetable Rolls with Rice Noodles

1/2 lb. shiitake mushrooms 

2 tsp. canola or peanut oil 

1 garlic clove, minced 

1 tsp. soy sauce, plus more for serving 

7 oz. thin dried rice noodles 

12 to 16 rice-paper wrappers 

1 red bell pepper, seeded and thinly sliced  

2 avocados, pitted, peeled and sliced 

1 head butter lettuce, torn into bite-size pieces 

2 carrots, peeled and julienned 

1 cup loosely packed mixed fresh herb sprigs, such as mint, cilantro and basil 

Asian red chili sauce for serving 

Asian peanut sauce for serving