Prepare the vegetables: Thinly slice the garlic and chop the bell peppers into one-inch pieces. Peel and chop the potato into roughly two-thirds of an inch pieces.
Make the sauce: Prepare the Dakbokkeumtang paste with oyster sauce, gochugaru, gochujang, rice vinegar, and black pepper.
Cook the chicken: Use bone-in, skin-on chicken thighs and breasts, cutting the breasts into 1-inch cubes. Heat oil in a pot over medium-high heat, and cook the chicken skin-side down for one minute to enhance flavor. Then, reduce to medium-low and add gochujang, gochugaru, onion, garlic, tomato paste, ginger paste, dark soy sauce, oyster sauce, rice vinegar, and black pepper. Add salt at the end, after tasting.
Braise the Chicken: Add one cup of water, along with potatoes and carrots, cover, and simmer for fifteen minutes. Then add zucchini and bell peppers, and simmer for another ten minutes, stirring every five minutes to prevent burning. Serve immediately; flavors improve the next day. Dakbokkeumtang is a wholesome dish.