Char the corn. Heat 1 tablespoon oil in a large pot over medium-high.
Add 3 cups of corn in a single layer. Cook undisturbed for 2–3 minutes to get some color, then stir and cook another 3–4 minutes until lightly charred in spots. Transfer to a bowl.
Repeat with the remaining 1 cup if needed, or save that cup for stirring in at the end for extra texture.
Sauté aromatics. Lower heat to medium. Add the remaining oil to the pot. Add onion with a pinch of salt and cook 4–5 minutes until softened.
Stir in garlic and jalapeño; cook 1 minute until fragrant.
Bloom the spices. Add chili powder, smoked paprika, and cumin. Stir for 30 seconds to wake up the spices.
Simmer. Return 3 cups of the charred corn to the pot. Pour in the broth, scraping up any browned bits.
Bring to a gentle simmer and cook 10–12 minutes to meld flavors.
Blend partially. Use an immersion blender to blend about half the soup in the pot, leaving some kernels whole. Or transfer 2–3 cups to a blender, blend until smooth, and return it to the pot. This gives you a creamy base with pops of corn.
Make it creamy. Stir in heavy cream, mayonnaise, and sour cream.
Simmer on low for 2–3 minutes. Do not boil, or the dairy can separate.
Finish with brightness. Stir in lime juice, cilantro, and half of the Cotija. Taste and adjust with salt, pepper, and more lime if needed.
If you saved the last cup of corn for texture, fold it in now and warm through.
Serve. Ladle into bowls and top with extra Cotija, cilantro, green onions, a sprinkle of chili powder or chili-lime seasoning, and a squeeze of lime. Add hot sauce if you like heat.