Trim any excess fat from the chicken. Season generously with salt on both sides. Set aside.
Heat oil over medium-high heat in a pot. Briefly sear the bananas on both sides, making sure they don't become mushy. Transfer them to a plate.
Next, lightly brown the carrots on both sides. Transfer them to a plate.
Add more oil, if needed. Sear the chicken, with its skin side down first, until lightly browned. Work in batches to achieve a nice crust, then transfer them to a plate.
Quickly sear the chorizo slices for about a minute to bring out their flavors. Once lightly browned, transfer to a plate.
Add more oil if needed and reduce to medium heat. Sauté the onion and garlic until softened.
Add the tomato paste and cook until it caramelizes and turns darker.
Pour in 2½ to 3 cups of water, depending on how thick or soupy you prefer the stew. Add the bay leaves, chicken base or bouillon, fish sauce, sugar, and some ground pepper.
Mix everything well, scraping up the fond (the browned bits) from the bottom of the pot for that extra flavor. Turn up the heat and bring the mixture to a boil.
Once the mixture is boiling, add the chicken back. Cover and simmer over medium heat for 30 minutes or until tender.
Add the chorizo, carrots, and chickpeas. Let them cook for another 10 minutes or until the carrots are tender.
Add the bananas, yardlong beans, bok choy, and cabbage. Cover and cook for 5 minutes to allow them to soften slightly. Taste and adjust as necessary, then turn off the heat.