Heat oil in a large, nonstick pot or cast iron Dutch oven until shimmering. Add corn kernels, chopped onion, chili powder, ½ teaspoon kosher salt, and ½ teaspoon black pepper. Cook over medium-high heat, stirring frequently, until onions are soft and corn is lightly charred in spots, about 8-10 minutes.

Add garlic and cook until fragrant, 1 minute. Remove 1-½ cups of corn mixture from the pot and set aside. Stir broth and 6 stripped corn cobs into the pot, scraping up the brown bits on the bottom. Bring to a boil, reduce heat, and simmer for 20 minutes.

Use tongs to remove corn cobs from pot and discard.

Stir sour cream and Cotija into the soup. Transfer soup to a blender or food processor (in batches for safety) to puree until smooth.

Return soup to pot and if needed, gently reheat to desired serving temperature. Stir in half (¾ cup) of the reserved corn mixture, lime juice, and 2 tablespoons chopped cilantro. Season to taste with salt, pepper, and chili powder.

Toss remaining ¾ cup corn with lime zest and 2 teaspoons chopped cilantro. Serve soup, topped with a few spoonfuls of the corn mixture, and an extra sprinkling of Cotija.