Start by preparing all your ingredients so cooking moves smoothly. Cut the chicken thighs into 1-inch pieces and set aside. Slice the large onion into 1/4-inch wedges, thinly slice the carrot into rounds, cut the celery on the diagonal, slice the shiitake mushrooms, and have the bamboo shoots and water chestnuts ready. Cut the green onions into 2-inch lengths and mince the ginger. In a bowl, whisk together the soy sauce, chicken stock, sake, mirin, and sugar—this is your braising liquid that will become the sauce for the entire dish.
Heat the vegetable oil in a large, heavy-bottomed pot or wok over medium-high heat. Working in batches if needed to avoid overcrowding, sear the chicken pieces until they develop a golden-brown color on all sides, about 5-7 minutes total. This browning step builds deep flavor through the Maillard reaction—don't skip it even though the chicken will finish cooking in the braising liquid. Once browned, set the chicken aside on a plate.
In the same pot, add the toasted sesame oil and minced ginger, stirring constantly for about 30 seconds until fragrant. This blooming technique releases the essential oils from the ginger and perfumes the entire dish. Immediately add the sliced onion, carrot, and celery, stirring frequently for 2 minutes to soften the vegetables slightly and allow them to absorb the ginger-infused oil. I like to keep these vegetables with a little bite—they'll continue cooking in the braising liquid, so you want them just starting to soften here.
Add the bamboo shoots, shiitake mushrooms, and water chestnuts to the pot, stirring to combine with the aromatics. Cook for another 2 minutes, allowing these vegetables to warm through and begin releasing their flavors into the oil. The combination of quick-cooking and slower-cooking vegetables creates layers of texture in the final dish.
Return the seared chicken to the pot and pour in the braising liquid from Step 1, stirring gently to distribute everything evenly. Bring the mixture to a simmer over medium heat and let it cook uncovered for 8-10 minutes, allowing the flavors to meld and the chicken to finish cooking through. The braising liquid will reduce slightly and coat everything with a glossy glaze. Meanwhile, prepare the bean thread noodles by boiling them in a separate pot of water for 5 minutes, then drain thoroughly—you want them tender but not mushy.
Add the cooked bean thread noodles from Step 5 and the green onions to the pot, stirring gently to combine everything without breaking apart the delicate noodles. Cook for just 1-2 minutes more to warm the noodles through and let the green onions wilt slightly. Taste the dish and adjust seasoning if needed—Hawaiian hekka should have a balance of salty, sweet, and savory flavors. Serve immediately in bowls with plenty of the braising liquid, as this stew-like dish is meant to be eaten with broth. I find that letting everything meld for those final 1-2 minutes brings all the flavors together beautifully—don't rush this step.