Cook egg noodles according to package instructions and drain. 

In a large skillet over medium-high heat, heat oil. Season chicken with salt and pepper. Add chicken and cook until golden and crispy, 7 to 8 minutes. Move chicken to one side of skillet, and to the other side, add garlic, ginger, carrot, and cabbage and cook until tender, 3 minutes.

Meanwhile, make sauce: In a medium bowl, whisk together broth, soy sauce, and oyster sauce. 

Pour sauce over skillet and add cooked noodles, tossing to combine.

Garnish with green onions and sesame seeds before serving.