Add 1 cup of beans and 1/2 cup broth to a blender and blend until smooth. Set aside
In a large pot over medium heat, add the olive oil , onion, and jalapeno. Saute for 3-5 minutes, until onion is translucent
Add garlic and saute for another 30 seconds
Add the pureed beans and broth, remaining chicken broth, remaining beans, diced green chilies, corn kernels, lime juice, cumin, chili powder, oregano, salt, pepper, smoked paprika, and cayenne pepper. Bring to a boil, then reduce the heat to a low to simmer.
Cook for 20 minutes, stirring occasionally, then remove from heat
Add chicken and greek yogurt to the pot, and stir to combine.
Divide between bowls and top with the monterey jack cheese. Serve.