Cook the Chicken: In a large pot or deep skillet, warm the vegetable oil over medium-high heat. Add the pieces of chicken thighs and sauté, stirring occasionally, until they are golden brown and fully cooked, approximately 5 to 7 minutes. Once cooked, take the chicken out of the pot and set it aside.
Sauté the Aromatics: In the same pot, add the sliced onion, minced garlic, and sliced ginger. Cook for 2-3 minutes until the onions are soft and fragrant.
Add the Vegetables: Add the sliced bell pepper, napa cabbage, broccoli florets, and carrots to the pot. Stir everything together and cook for about 5 minutes, until the vegetables are slightly softened but still crisp.
Make the Sauce: While the vegetables are cooking, whisk together the soy sauce, water, oyster sauce, sugar, and sesame oil in a small bowl.
Combine the Chicken and Sauce: Return the cooked chicken to the pot and mix it with the vegetables and sauce. Bring the mixture to a simmer. Stir in the cornstarch-water mixture and cook for another 2-3 minutes, until the sauce has thickened and coats the chicken and vegetables evenly.
Serve: Garnish the dish with chopped green onions. Serve the Chicken Hekka over cooked rice or noodles, allowing the sauce to soak into the grains or noodles for added flavor.