To make the sauce for these Thai-inspired kebabs, simply pulse cashews and curry paste together with water. Consider using other nuts, too, like peanuts or almonds for future dinners.
Soak eight 8-inch wooden skewers in water 15 minutes. In a food processor, pulse cashews with curry paste and 3/4 cup water until smooth. Combine 1 cup of cashew mixture with 1/3 cup water. Toss chicken with remaining mixture; lightly season with salt. Meanwhile, bring a large pot of water to a boil. Cook noodles until just tender, about 2 minutes; drain. Rinse with cold water; drain well.
With a vegetable peeler or mandoline, shave cucumber and carrots into wide, paper-thin ribbons. Heat a grill or grill pan to medium-high; lightly brush with oil. Thread chicken onto skewers; grill, in batches if needed, 6 to 8 minutes per side, transferring to a plate as done. Serve, with noodles, lettuce, cucumber, carrots, cashew sauce, chopped cashews, and lime wedges.
If the cooked noodles stick together, rinse them under cold water again before serving and drain well.