Bring a medium pot of salted water to a boil. Add the chicken breast and cook until tender and cooked through, about 25 minutes. Transfer to a plate, cool slightly, then shred into bite-size pieces.
Place the glass noodles in a large bowl and cover with hot water. Soak until softened, about 6 minutes. Drain well and cut into shorter strands.
Add the cabbage, cucumbers, carrots, green onions, bean sprouts, red onion, chili pepper, chicken, cilantro, mint, and peanuts to a large bowl.
Whisk the peanut butter, coconut cream, soy sauce, honey, garlic, ginger, lemon juice, and salt until smooth.
Pour the dressing over the salad and toss until evenly coated. Transfer to a serving platter and finish with chopped peanuts and chili pepper.