Cook the Asian-style noodles according to package instructions until al dente; drain and set aside.
Whisk together chicken broth, soy sauce, brown sugar, Sriracha, red chili paste, and minced ginger in a bowl to make the sauce; set aside.
Heat the sesame oil in a large skillet or wok over medium-high heat.
Add the sliced mushrooms and cook about 5 minutes, stirring occasionally, until they begin to brown.
Add the sliced red and green bell peppers and minced garlic; cook another 3 minutes until peppers begin to soften.
Add the cooked, chopped chicken to the skillet and toss to combine.
Pour the prepared sauce into the skillet and stir; bring to a boil and cook for about 2 minutes to slightly reduce and coat the ingredients.
Add the cooked noodles to the skillet and toss thoroughly so the noodles absorb the sauce; taste and season with the 1/4 teaspoon salt and 1/4 teaspoon pepper if needed.
Remove from heat and garnish with chopped green onions and chopped peanuts, then serve.