Bring a large pot of water to a boil for the rice noodles.
In a food processor, pulse the herbs, peanut butter, about 3 tbsp. oil, 2 tbsp. fish sauce, garlic, chiles, ginger, lime juice and brown sugar to make the pesto. Transfer the pesto to a large, shallow serving bowl.
In a large skillet, heat the remaining 1 tbsp. oil over high. Stir-fry the shrimp until just cooked through, 3 minutes. Season with fish sauce and pepper.
Add the noodles to the boiling water; cook until tender. Stir about 3/4 cup pasta cooking water into the pesto to thin. Drain the noodles, then toss with the pesto and most of the shrimp. Toss in the lettuce. Serve in shallow bowls, topped with the rest of the shrimp.