Char the Corn: In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the corn and cook, undisturbed, until lightly charred in spots, about 3-4 minutes. Stir and cook 2-3 more minutes, stirring once or twice. Remove to a bowl and set aside.
Sauté the Base: To the same pot (no need to wash it first), heat the butter over medium heat. Add the onion and ¼ teaspoon of the salt. Sauté for 3-4 minutes until softened. Sprinkle it with the garlic, chili powder, and smoked paprika. Cook until fragrant, about 30 seconds, stirring frequently.
Add the Chicken & Simmer: Add the chicken, broth, white beans, charred corn, and 1 teaspoon of salt. Cover, bring to a boil, then reduce to a gentle simmer. Cook, covered, for 20-30 minutes, or until the chicken is cooked through and tender (timing will depend on the type of chicken and size of pieces used).
Partially Blend: Turn off the heat. Remove the chicken to a cutting board and shred with two forks or dice into 1-inch chunks. Use an immersion blender to blend 1 to 2 cups of the soup directly in the pot. Alternatively, carefully transfer to a blender, blend on high, then return to the pot. This helps create a thicker, creamier base without added cream, while keeping plenty of texture,
Add Remaining Ingredients: Ladle one cup of the soup broth to a small bowl. Stir in the cream cheese and whisk until fully melted and smooth. Add the cream cheese mixture along with the crumbled cotija (or feta) and cooked chicken back to the pot, stirring to combine.
Add the lime juice, stir, then taste and add more salt if needed. Ladle into bowls and top with more cotija and whatever else makes you happy!