Prepare the corn by cutting kernels off the cob if using fresh corn, or measure out four cups if using frozen or canned corn.
Heat olive oil in a large pot over medium heat. Sauté diced onion for about 5 minutes until translucent, then add minced garlic and cook for an additional 1-2 minutes.
Add corn and broth to the pot, along with chili powder, smoked paprika, cumin, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Use an immersion blender to puree the soup until smooth, or blend only half for a chunkier texture.
Stir in heavy cream and let simmer for another 5 minutes. Remove from heat and add chopped cilantro and lime juice. Adjust seasoning if needed.
Serve hot, garnished with crumbled cotija cheese and sliced jalapeños.