In a large Dutch oven, heat the olive oil over medium heat.
Add the onion and poblano pepper. Cook for 5 to 6 minutes, stirring occasionally, until softened.
Add the garlic, chili powder, cumin, smoked paprika, and black pepper. Cook for 30 seconds.
Add the chicken broth, 3 cups of corn, shredded chicken, green chiles, and white beans. Using a wooden spoon, stir well.
Bring the soup to a boil. Reduce the heat to medium-low. Simmer uncovered for 15 minutes.
In a blender, place the remaining 1 cup of corn and the cottage cheese. Blend until mostly smooth.
Stir the blended corn mixture into the soup.
Reduce the heat to low.
Add the Greek yogurt and Monterey Jack cheese. Stir until the cheese melts and the soup is creamy.
Stir in the lime juice and half of the cotija cheese.
Top each serving with the remaining cotija cheese and cilantro.
Notes
Tips and Tricks
Let the yogurt warm slightly - Cold Greek yogurt is more likely to separate. Let it sit at room temperature for about 15 minutes before adding it.Adjust the texture - Blend the corn and cottage cheese longer for a smoother broth. Leave it slightly coarse if you want more corn texture.Keep garnishes separate - Store the cotija cheese and cilantro separately if you plan to save leftovers.
Storing and Reheating
Store in the refrigerator - Place the cooled soup in an airtight container and refrigerate for up to 4 days.Freeze the soup - Freeze in airtight containers for up to 2 months. The dairy may separate slightly after thawing.Reheat on the stovetop - Place the soup in a saucepan and warm over low heat, stirring often. Avoid boiling it because high heat can cause the yogurt to separate.Reheat in the microwave - Heat one serving in a microwave-safe bowl in 30-second intervals, stirring between each interval.