Using a vegetable peeler or mandoline, shave the cucumber lengthwise into thin ribbons.
Place in a bowl, sprinkle lightly with salt, and let sit for 5–10 minutes. Gently pat dry to remove excess moisture.
Bring a large pot of water to a boil. Cook the brown rice noodles according to package directions until just tender, slightly al dente. Drain immediately and rinse under cold running water until completely cooled. Toss lightly with a little bit of sesame oil to prevent sticking and set aside.
In a large mixing bowl, whisk together the coconut milk, peanut butter, red curry paste, tamari, rest of the sesame oil, rice vinegar, lime juice, ginger, and garlic until completely smooth and creamy.
Taste and adjust seasoning if needed, add more lime for brightness or curry paste for heat.
Add the chilled noodles to the coconut curry sauce and toss until fully coated.
Fold in the cucumber ribbons gently so they stay crisp and visible throughout the noodles.
Divide into bowls and top with green onions, fresh cilantro, sesame seeds, Chili crisp or chili oil and lime wedges. Serve immediately chilled or slightly cool.