Cook the ramen noodles according to package instructions in a large pot, then reserve 1 cup of the cooking water and drain the noodles.
In a small bowl, whisk together soy sauce, oyster sauce, sriracha, honey, and sesame oil until smooth to make the sauce.
Heat the 12-inch skillet over medium heat and melt the butter.
Add the sliced chicken to the skillet, season with half the pepper, and cook until browned on one side, about 3–4 minutes; flip, season the other side with the remaining pepper, and cook until cooked through, about 3–4 more minutes.
Add the sliced red bell pepper to the skillet and cook 2–3 minutes until slightly softened.
Stir in the minced garlic and cook 30–45 seconds until fragrant.
Add the shredded napa cabbage and cook about 2 minutes until wilted and starting to brown.
Toss in the cooked ramen noodles and pour the prepared sauce over everything; add a splash of the reserved cooking water as needed to loosen and help coat the noodles.
Stir in the sliced green onions, cook for 1 minute more to heat through, then remove from heat.
Serve hot, sprinkled with sesame seeds if using.