Cook the angel hair pasta according to package directions. Drain and set aside.
Make the sauce: In a saucepan over medium heat, combine the light coconut milk, creamy peanut butter, and chicken broth. Stir constantly until smooth and heated through, but do not boil.
Add the soy sauce, brown sugar, minced garlic, ground cumin, and curry powder to the saucepan. Season with salt and cayenne to taste and continue stirring until the sauce thickens slightly to the consistency of a thin spaghetti sauce. Remove from heat and cover.
Heat 1 tablespoon of sesame oil in a large skillet over medium-high heat. Add the chicken chunks and stir-fry until nearly cooked through.
Squeeze some of the lime (or lemon) juice into the pan while the chicken cooks to add moisture as needed.
Reserve about 1/2 cup of the sliced green onions for garnish. Add the remaining green onions and the shredded carrot to the skillet with the chicken and stir-fry until the vegetables are tender and the chicken is fully cooked. Add more lime juice if needed for moisture.
Spoon about 1/2 to 1 cup of the peanut sauce into the skillet and toss the chicken and vegetables to coat.
Portion the cooked pasta onto plates (or toss the pasta with some sauce if you prefer). Ladle the chicken and vegetable mixture over the pasta and drizzle additional peanut sauce as desired.
Garnish each serving with reserved green onions, a sprinkle of cayenne pepper to taste, and chopped peanuts if desired.