Season the cubed chicken with salt and pepper, drizzle with 1 teaspoon sesame oil, and set aside.
Cook the rice noodles according to the package instructions, drain, and set aside.
Heat a large wok or skillet over medium-high heat and add 1 1/2 tablespoons of the olive oil.
Add the chicken and sauté until cooked through, about 4–5 minutes, then transfer to a plate.
Return the pan to the heat and add the remaining 1 1/2 tablespoons olive oil.
Add broccoli, grated carrots, sliced bell pepper, minced garlic, and minced ginger; cook, stirring, until vegetables are crisp-tender, about 2–3 minutes.
In a small bowl, whisk together soy sauce, brown sugar, hoisin sauce, cornstarch, and water until smooth.
Pour the sauce into the pan with the vegetables, return the cooked chicken, and add the prepared noodles.
Cook, stirring frequently, until the sauce bubbles and thickens and everything is well coated, about 1–2 minutes; stir in red chili flakes if using and adjust seasoning with salt and pepper to taste.
Serve hot topped with toasted sesame seeds and thinly sliced green onions.
