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1 small (10-ounce) sweet potato, peeled and cut into 3/4-inch pieces (about 1 3/4 cups)
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1 small (8-ounce) turnip, peeled and cut into 3/4-inch pieces (about 1 1/4 cups)
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3 tablespoons canola oil, divided
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¾ teaspoon kosher salt, divided
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½ teaspoon black pepper, divided
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1 large (1 1/2-ounce) shallot, finely chopped (about 1/4 cup)
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3 tablespoons minced peeled fresh ginger (from 1 [3-inch] piece ginger)
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4 medium garlic cloves, finely chopped (about 1 1/2 tablespoons)
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1 lemongrass stalk (pale core only), finely chopped (about 1 1/2 tablespoons)
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2 fresh red Thai chiles (unseeded), finely chopped (about 1 teaspoon)
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¼ cup green curry paste (such as Maesri or Thai Kitchen)
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2 cups turkey broth or chicken broth
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1 (13.66-ounce) can unsweetened coconut milk
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2 tablespoons fresh lime juice (from 1 large lime), plus more to taste
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2 teaspoons fish sauce
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2 cups firmly packed fresh curly leaf spinach, torn, or stemmed Swiss chard, torn
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1 ⅓ cups shredded cooked turkey breast (about 8 ounces)
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Fresh basil leaves, for garnish