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Bring water to a boil in a large pot to prepare the noodles while you are working on the chicken.
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Choose a large, heavy-bottomed pot (like a Dutch oven) and heat over medium high heat with the vegetable oil. When it is hot, add the chicken pieces in a single layer; you will probably need to do this in 2 batches. Brown the chicken on each side, 5-8 minutes per side, before removing to a bowl.
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While the chicken is browning, whisk up the sauce ingredients. Set aside.
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When the chicken is removed, add the onions to the pot. Add a splash of water if there are lots of stuck chicken bits to the bottom of the pan. Sprinkle with a pinch of salt. Cook, stirring occasionally, until the onions are starting to caramelize.
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Add the garlic and cook for 1-2 minutes.
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Add the whisked sauce into the pot and bring to a boil. Then add the chicken back into the pot, along with any accumulated juices. Mix the chicken into the sauce and then cover the pot. Reduce the heat to maintain a gentle simmer. Let cook for 10 minutes.
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Add the zucchini, summer squash and bell pepper. Stir into the dish and bring the liquid back to a boil. Once again cover and reduce the heat to maintain a gentle simmer. Cook for 5 minutes.
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Toss the green beans on top of the chicken and vegetables. Bring the liquid back to a boil, and then again cover and reduce heat to maintain a simmer. Cook until the green beans are steamed to your liking (we like them pretty crisp); by now the chicken should also be done.
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Add the cooked noodles to the pot and stir them into the dish. Mix in the chopped cilantro.
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Taste the dish for additional salt or brown sugar. Serve hot, with gojuchang on the side for those who like their dishes spicy.