Prep the chicken. Trim excess skin and fat. Rinse quickly and pat dry.
For cleaner flavor, you can parboil the chicken for 3–4 minutes, then drain and rinse.
Make the sauce. In a bowl, mix gochujang, gochugaru, soy sauce, garlic, ginger, rice syrup (or sugar), sesame oil, and mirin if using. Aim for a thick, glossy paste.
Start the pot. Place chicken in a wide pot. Add onions, potatoes, carrots, and optional daikon.
Pour the sauce over and add water or stock until it comes about two-thirds up the ingredients.
Simmer gently. Bring to a boil over medium-high heat, then lower to a steady simmer. Cover and cook for 15 minutes, stirring once to prevent sticking.
Uncover and reduce. Remove the lid and simmer another 15–20 minutes until the potatoes are tender and the sauce thickens. If you like it thicker, stir in a slurry of potato starch or cornstarch with a splash of water.
Finish and season. Add green onions and fresh chilies in the last 2–3 minutes.
Taste and adjust with a pinch of salt, a splash of soy, or a touch more sugar to balance the heat.
Serve hot. Spoon into bowls and serve with steamed white rice. A side of kimchi or pickled radish cuts through the richness.