Preheat the broiler. Line a baking sheet with foil.
Toss the chicken breasts with 1 tablespoon of the honey, 1 tablespoon of the sesame oil, 1/2 teaspoon salt and several grinds of black pepper in a medium bowl. Transfer the chicken to the prepared baking sheet and broil, flipping halfway, until cooked through, about 10 minutes.
Meanwhile, bring a large pot of salted water to a boil. Cook the ramen for as long as specified on the package directions, then drain in a colander and set aside.
Whisk 2 tablespoons of the rice vinegar with 1 tablespoon sesame oil in a large bowl. Add the green beans, cabbage, herbs and carrots and toss to coat.
Whisk together the peanut butter, sriracha, 1/3 cup warm water, the remaining 2 tablespoons honey and remaining 1 tablespoon each sesame oil and vinegar in a large bowl until well combined. Season with salt. Add the noodles and toss to combine.
Thinly slice the chicken. Divide the noodles among 4 bowls and top with the green bean slaw, chicken and peanuts.
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