Melt the butter in a large pot over medium heat.
Add the onion and cook for 4 to 5 minutes until softened.
Stir in the garlic and cook for another 30 seconds.
Add the chicken broth, corn, shredded chicken, diced tomatoes with green chilies, chili powder, smoked paprika, cumin, salt, and black pepper.
Bring the soup to a gentle simmer and cook for 15 to 20 minutes.
Stir in the cream cheese until completely melted.
Pour in the heavy cream and stir until smooth.
Remove the soup from the heat and stir in the lime juice.
Serve topped with crumbled cotija cheese, fresh cilantro, and extra chili powder if desired.