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Sprinkle chicken on both sides with sea salt. Set a deep 10-inch skillet over medium-high heat. Add oil, and when hot, add chicken. Sauté, nudging slightly to prevent sticking, for 7 minutes. Flip, and sauté another 5 minutes or until internal temperature reaches 165 degrees F. Set cooked chicken in a medium bowl and set aside.
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Pour off all but 2 tablespoons accumulated fat and edge heat down to medium. Add shallots, ginger, chilies, garlic, and a generous pinch of sea salt, and sauté until soft, 5 - 7 minutes. Add mushrooms and a splash of stock. Use a wooden spoon to scrape up any brown bits; then add remaining stock, lime zest and lemongrass stalk. Bring mixture to a boil, and then turn heat down to a gentle simmer. Taste, and adjust salt levels as needed. Cook for 20 minutes.
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Meanwhile, cook rice noodles according to package instructions.
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When chicken is cool enough to handle, cut into 1/2-inch thick slices and add to curry. When 5 minutes of cook time remain, stir in coconut milk and basil.
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Ladle over rice noodles and garnish with a squeeze of lime juice, green chili slices, and basil and cilantro leaves. Serve immediately.