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Whisk together coconut milk, chicken stock, curry paste, brown sugar, fish sauce, ginger paste, and lemongrass paste in a bowl.
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Heat a large wok or skillet over high heat. Add 1 tablespoon oil and swirl pan to coat. Add shrimp and stir-fry until opaque, about 3 to 4 minutes. Remove shrimp from pan.
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Add remaining 1 tablespoon oil to the pan. Add vegetables and stir-fry until crisp-tender, about 4 minutes.
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Pour curry sauce over the vegetables. Bring to a boil and cook for 4 minutes.
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Stir in shrimp and basil. Cook for an additional minute or until shrimp is cooked through.
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Divide rice into 4 bowls and top with Thai shrimp curry. Serve with lime wedges.