Cook the soba noodles according to the package directions. Drain, then rinse under cold water to stop cooking and prevent sticking. Set aside to drain well.
Make the peanut sauce: In a small bowl or jar, whisk together peanut butter, soy sauce (or tamari), rice vinegar, lime juice, honey, sesame oil, sriracha, and grated ginger. Add warm water 1 tablespoon at a time until the sauce is creamy and pourable. Stir in red pepper flakes if using.
If cooking chicken fresh: Season chicken with salt, pepper, and chili powder. Cook in a skillet over medium-high heat until cooked through (about 6–7 minutes per side, depending on thickness). Rest 5 minutes, then slice or dice.
Assemble the salad: Add drained soba noodles to a large mixing bowl. Add bell pepper, carrots, scallions, and cilantro. Pour in about half the peanut sauce and toss until evenly coated.
Top with chicken. Drizzle with remaining peanut sauce (as needed) and sprinkle with crushed peanuts. Serve right away, or chill for about 30 minutes for a colder noodle salad.