Whisk together the miso, sesame oil, brown sugar, and lime juice, and garlic until smooth. Slowly stream in oil, whisking to emulsify. Whisk in water 1 Tbsp. at a time until dressing is consistency of heavy cream.
Add noodles to the sauce, tossing to coat. Add chile, cucumber, and scallions; season with salt and pepper. Toss to evenly distribute.