Preheat your oven to 425 degrees F.
Char the whole jalapeños by holding them over the open flame of your stove and rotating them until they’re dark on all sides. If you don’t have a gas stove, you can place them whole on a broil-safe sheet pan and broil them on high for a few minutes until charred. Watch them carefully.
Place the charred jalapeños in a bowl and cover the bowl with plastic wrap. Allow them to sit for 5 minutes before removing them from the bowl. Peel off the skin of the jalapeños and remove the inner ribs and seeds. Set them aside.
On a sheet pan, add your diced onions, green pepper, garlic, olive oil, and cumin. Mix it around to coat it all evenly in the oil and cumin. Place the sheet pan in the oven and roast until the onions and pepper become soft, about 10 minutes.
Add the cooked onions, pepper, and garlic to the slow cooker. Top them with the chicken breasts, corn, 1 can of the canned green chiles, 1 can of the beans, and 1 can of chicken broth.
To a blender, add the other cans of green chiles, beans, and chicken broth, along with the charred jalapeños. Blend until smooth and add the mixture to the rest of the ingredients in the slow cooker. Season with salt and pepper.
Mix everything together. Cover the slow cooker and cook on high for 3 hours or on low for 6 hours. When done, remove the chicken, shred it with two forks, and place it back into the slow cooker.
Serve individually and top with fresh lime juice, cheddar cheese, sliced jalapeños, and tortilla chips.