Spaghetti with Shrimp Rundown Sauce

Ingredients

• ¾ cup extra-virgin olive oil, divided
• 1 lb. shrimp shells (5 cups), plus 1 lb. medium shrimp, peeled, deveined, and butterflied, divided
• One 2-oz. piece ginger, bruised and coarsely chopped (¾ cup)
• 1 medium stalk of lemongrass, bruised and thinly sliced (⅓ cup)
• 1 habanero chile, quartered
• 3 oz. tomato paste
• 4 cups full-fat coconut milk (32 oz.)
• 1 Tbsp. finely grated orange zest
• 2 tsp. finely grated lemon zest
• 1 tsp. finely grated lime zest
• ¼ cup thinly sliced scallions
• Kosher salt
• 1½ lb. fresh spaghetti (or substitute 1 lb. dried spaghetti), boiled in a pot of salted water until halfway cooked, then drained and rinsed in cool water, cooking water reserved
• 1 tsp. finely chopped fresh mint
• 1 tsp. finely chopped flat-leaf parsley
• 1 tsp. finely chopped fresh basil

Instructions

1. In a wide pot over medium-high heat, add 2 tablespoons oil. Once the oil is hot, add the shrimp shells and cook, stirring frequently, until bright pink, 2–3 minutes. Add the ginger, lemongrass, and habanero; cook, stirring frequently, until very fragrant, 4–5 minutes. Stir in the tomato paste, reduce the heat to medium, and continue cooking and stirring until completely combined and very dry but not yet caramelized, 6–8 minutes more. Add the coconut milk and 8 cups cold water, increase the heat to medium-high, and bring to a boil. Lower the heat to maintain a strong simmer, then cook, stirring occasionally, until the mixture is reduced by about a third, 45–50 minutes.
2. Meanwhile, marinate the shrimp: In a medium bowl, add the shrimp, ½ cup oil, and citrus zests; toss well to coat. Refrigerate until you are ready to finish the pasta, at least 45 minutes or up to 4 hours.
3. Set a fine-mesh strainer over a large, heatproof liquid-measuring cup or bowl. Strain the shrimp-shell stock, pressing on the solids with a ladle to extract as much liquid as possible. Discard the solids, then measure 2 cups of the stock and set by the stove. (Reserve the remaining stock for another use; it can be refrigerated for up to 3 days or frozen for up to 3 months.)
4. In a deep, wide skillet over medium heat, add the remaining 2 tablespoons oil. Once the oil is hot, add the scallions and cook, stirring frequently, until softened, 2–3 minutes. Add the reserved 2 cups stock and bring to a strong simmer; cook, stirring frequently, until the stock is reduced by half and beginning to separate, 8–10 minutes. Season with salt. Add the pasta and shrimp, and cook, stirring and tossing continuously with tongs, until the shrimp and pasta are cooked through, and the sauce is thick and creamy, 3–5 minutes. (If the sauce looks dry, add reserved pasta cooking water as needed.) Transfer to a platter, sprinkle with herbs, and serve hot.