Season the chicken pieces all over with salt and pepper.
Heat the vegetable oil in a large pot or deep skillet over medium-high heat. Brown the chicken on all sides, about 5–7 minutes per side, then remove and set aside.
Add the chopped onion to the same pot and cook until softened, about 5 minutes. Stir in the minced garlic and cook 1–2 minutes until fragrant.
Pour a little chicken broth into the pot to deglaze, scraping up browned bits. Add the cubed potatoes and sliced carrots and cook 3–4 minutes, stirring occasionally.
Add the sliced red and green bell peppers and sauté 2–3 minutes until they begin to soften.
Pour in the tomato sauce and remaining chicken broth. Return the browned chicken to the pot and add soy sauce, bay leaf, and sugar (if using). Stir to combine.
Bring to a boil, then reduce heat to low. Cover and simmer for 25–30 minutes, or until the chicken is cooked through and vegetables are tender.
Stir in the green peas during the last 5 minutes of cooking to heat through. Remove and discard the bay leaf.
Garnish with chopped green onions and serve hot.
