Soften the Onions and Jalapeños: Heat a little bit of olive oil in a large pot or Dutch oven set over medium-high heat. Once hot, add the diced onion and jalapeños and cook until softened, then add the minced garlic. Cook until fragrant.
Add the Seasoning and Broth: Add the canned green chiles, cumin, chili powder (not cayenne pepper), oregano, salt, and black pepper. Stir well then add the chicken stock to the pot.
Cook the Chicken: Add the chicken to the pot and bring to a boil, then immediately reduce to a simmer and cover. Cook just until the chicken is cooked through.
Puree One Can of Beans: Meanwhile, puree one can of white beans in a small food processor and drain and rinse the other can in a fine-mesh strainer.
Remove and Shred the Chicken. Set aside.
Add the Corn, Beans, and Cream Cheese: Simmer gently for about 10-15 minutes, then add the shredded chicken to the pot.
Season: Add the fresh lime juice and cilantro, and season with additional salt and black pepper, to taste.