Heat olive oil in a large pot over medium heat. Add diced onion and cook until translucent.
Stir in minced garlic and cook for another minute until fragrant.
Add corn, chili powder, smoked paprika, cayenne, and a pinch of salt. Cook for 5–6 minutes, stirring occasionally.
Pour in the vegetable broth and bring to a boil. Reduce heat and let simmer for 10 minutes.
Use an immersion blender to partially blend the soup (or blend half in a regular blender and return to pot).
Stir in heavy cream, sour cream, and crumbled cotija cheese. Simmer for 5 more minutes.
Season with lime juice, salt, and pepper to taste.
Serve hot, garnished with cilantro and extra cotija cheese.