Finely chop up the bell pepper and onion. Mince the garlic. In a medium to large pot, heat the olive oil over medium/high heat. Cook the onion and bell peppers, seasoning well with salt and paper and a little bit of cayenne. Cook until beginning to soften, 2-3 minutes. Add the garlic and cook another minute. Then stir in the green chilies.
Turn the heat down to medium low and add the stock as well as one can of (drained) beans. Cover and cook for 5-6 minutes until everything is nice and hot. Then use an immersion blender (or in a blender in batches) to blend the soup together. You don't necessarily want it perfectly smooth, more of a rough blend (this is the texture I prefer). Then stir in the remaining beans, Greek yogurt, and cilantro and continue to cook until everything is warm. Serve with more cilantro, shredded cheese, and chips.
The leftover soup may separate some when stored in the refrigerator. But just give it a good stir when you rewarm it and all will be well in the world.