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1
Heat 1 and 1/2 tablespoons of the oil in a 5- to 6-quart Dutch oven over medium-high heat until shimmering hot.
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2
Season the chicken with 1/2 teaspoon each salt and pepper, and cook without disturbing until its browned and releases easily from the bottom of the pot, about 2 minutes.
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3
Flip and cook until the second side is browned and almost firm to the touch (just short of cooked through), about 2 minutes.
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4
Transfer the chicken to a cutting board to cool.
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5
Add the remaining 1 tablespoon oil and the shallots to the pot.
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6
Sprinkle with 1/4 teaspoon salt, reduce the heat to medium and cook, stirring, until the shallots start soften, about 2 minutes.
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7
Stir in the lemongrass, ginger, and brown sugar and cook, stirring, until the ginger and lemongrass sizzle and become fragrant, about 1 minute.
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8
Add the chicken broth, scraping up any browned bits from the bottom of the pot, and raise the heat to medium high.
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9
Bring the broth to a boil and then reduce to a simmer.
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10
Add the mushrooms, and cook, stirring occasionally, until tender, 5 to 7 minutes.
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11
Meanwhile, bring a medium pot of well-salted water to a boil and cook the noodles, stirring, until just tender, about 3 minutes.
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12
Transfer to a colander and run under cold water to cool slightly.
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13
Drain well.
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14
Use your fingers or the tines of a fork to shred the chicken.
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15
Add the chicken and noodles to the broth and cook until the noodles are completely tender and the chicken is cooked through, about 2 minutes.
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16
Discard the lemongrass.
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17
Stir in the chiles, torn basil, lime juice, and soy sauce; season with more soy to taste.
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18
Divide the noodles among 4 large, deep bowls.
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19
Ladle the soup over the noodles, and garnish with the basil sprigs and scallions, carrot, and cilantro.
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20
Serve with the lime wedges for squeezing.