Bring a large pot of salted water to a rolling boil.
Whisk together the peanut butter, soy sauce, lime juice, sesame oil, rice vinegar, chili garlic paste, honey, grated ginger, and 3 tablespoons hot water in a bowl until smooth; add more hot water if you prefer a thinner sauce.
Add the spaghetti to the boiling water and cook until al dente according to package directions.
Drain the noodles in a colander, then transfer them to a large bowl while still warm.
Add the shredded chicken, sliced red bell pepper, sliced green onions, chopped cilantro, and chopped basil to the bowl with the noodles.
Pour the peanut sauce over the noodles and toss thoroughly until everything is evenly coated.
Transfer to serving plates and garnish with chopped peanuts and sesame seeds, then serve immediately.
