In a small pot, add the broth and corn cobs. Bring to a boil, then simmer for 15 minute. Once simmered, remove the cobs and transfer the broth to a blender.
As the broth simmers, cook the shallots and corn. In a medium pot, add the olive oil over medium-high heat. Once shimmering, add the shallots and season with salt. Sauté for 6 minutes, then add the corn kernels. Season with another pinch of salt and cook until the corn has softened and brightened in color—8 more minutes. Add the turmeric and stir until fragrant, then add the coconut milk. Bring to a boil, then reduce heat and simmer for 15 minutes. Transfer to the blender with the broth and blend on high until smooth. Add the zest and lime juice and blend once more. Transfer to a container and refrigerate until cooled, or serve warm.(see note).
Cook the shrimp:
Make the marinade: In a small food processor, combine the olive oil, cilantro, black pepper, salt, garlic, and lemon juice. Blend until combined, then taste for salt.
Add the shrimp to a medium mixing bowl and sprinkle with a pinch of salt. Pour over the marinade and toss to coat. Refrigerate 20-30 minutes.
Heat a cast iron skillet to medium-high and add 2 Tbsp neutral oil. Once shimmery, add the shrimp and cook 1 1/2-2- minutes per side, or until no longer opaque and just beginning to curl (but be careful to not overcook to the point where the shrimp becomes a tight “o” shape).
Allow shrimp to cool if you’re serving soup chilled.
Pour the chilled soup into bowls and top with shrimp, cucumber, pickled red onion, toasted nuts, and herbs. Squeeze with fresh lime and enjoy!