2 medium scallions, sliced into rounds, for garnish (optional)
½ cup shredded carrots, for garnish (optional)
½ cup fresh cilantro leaves, for garnish (optional)
Heat 1 tablespoon of the oil in a large saucepan or Dutch oven over medium-high heat. When the oil is very hot, carefully add the shrimp and stir. Season with ½ teaspoon of the salt and pepper. Saute until almost cooked through (the shrimp will finish cooking later). Remove to a dish and set aside.
Add the remaining 1 tablespoon oil to the pan. Add the shallots and season with the remaining ¼ teaspoon salt. Reduce the heat to medium and sauté until the shallots are tender, about 2 minutes. Add the lemongrass, ginger, and brown sugar and cook, stirring, until very fragrant, about 1 minute.
Add the vegetable broth, scrapping the bottom of the pan to release the flavorful brown bites. Raise the heat to medium high and cook just until the soup boils, and then reduce to a simmer. Add the mushrooms, water chestnuts, bean sprouts, and bok choy. Cook, stirring occasionally, until the vegetables are tender, 5 to 7 minutes.
Meanwhile, bring a separate pot of water to a boil over high heat. Add the udon noodles and cook according to package instructions until al dente. Drain.
Add the shrimp and udon noodles to the soup and cook until the noodles are completely tender and the shrimp are cooked through, 2 to 3 minutes. Discard the lemongrass stalks and stir in the soy sauce and basil.
Divide the noodles and shrimp among 5 soup bowls. Ladle the broth over them and garnish with scallions, carrots, and cilantro, if using.
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