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In a large frying pan heat oil over medium heat.
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Add the onion and cook until slightly softened, about 3 minutes. Add any crunchy vegetables that will need longer cooking than others (I usually add the carrots at this point and wait on the beans and squash for a couple of minutes).
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Add the chicken and salt and pepper the whole mix. Cook for 2-3 minutes, until the chicken is cooked on the outside.
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Stir the curry paste into the pan and cook for about 30 seconds.
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Add coconut milk, broth, and fish sauce.
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Bring to a simmer, stirring occasionally, scraping up the browned bits on the pan bottom, cooking until vegetables are as soft as you'd like them to be and chicken is cooked through. Whisk together the cornstarch and water until smooth and pour it in to the pan, stirring constantly. After about thirty seconds, it should have thickened up a little.
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Add lime juice, salt and pepper to taste, and then serve over rice.