In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the corn kernels, vegetable broth, chili powder, cumin, smoked paprika, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Using an immersion blender, blend the soup until smooth. If you prefer a chunkier texture, blend only half of the soup and leave the rest as is.
Stir in the heavy cream and heat through, but do not boil.
Remove from heat and mix in the crumbled cotija cheese, chopped cilantro, and lime juice.
Serve hot, garnished with additional cotija cheese, cilantro, and sliced jalapeños if desired.