Cut the Corn Stand each ear upright in a wide bowl and cut the kernels off with a sharp knife. If using frozen corn, thaw fully and pat dry.
Build the Base Heat olive oil in a large pot over medium heat. Add onion and cook 5 minutes until soft. Add garlic and jalapeño, cook 2 more minutes. Stir in cumin and smoked paprika and cook 30 seconds.
Add the Corn Add corn kernels and stir to combine. Pour in vegetable broth and bring to a gentle boil. Reduce heat and simmer for 15 minutes, stirring occasionally.
Blend Use an immersion blender to blend about half the soup directly in the pot. For smoother results, blend more. Stir in coconut milk and simmer 5 more minutes.
Season Add lime juice, salt, and black pepper to taste. Adjust consistency with a splash of broth if too thick.
Serve Ladle into bowls. Top with red onion, jalapeño slices, cilantro, chives, and cracked black pepper. Serve immediately.