Whisk garlic, rice vinegar, soy sauce, fish sauce, brown sugar, Sriracha, hoisin, and sesame oil together in a mixing bowl for the dressing.

Tear chicken apart into strands similar in width to the spaghetti. Refrigerate until ready to use.

Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain and rinse with cold water.

Transfer spaghetti to a mixing bowl; add the chicken, carrots, bell pepper, and green onions. Pour in the dressing and toss by hand until well combined. Seal the surface of the salad with plastic wrap and refrigerate, tossing occasionally, for 2 to 12 hours, the longer the better.

Add peanuts, basil, mint, and cilantro to the salad. Toss well; taste and adjust for seasoning.