PREP: Spray a large slow cooker (I use a 6-quart one) with nonstick spray. Trim the fat off of the breasts or thighs. If you are using breasts, cut each breast into 2-3 pieces.
SLOW COOKER: Add the chicken, garlic, creamed corn (undrained), fire-roasted corn (drained), drained and rinsed black beans, undrained diced green chiles, chipotle chili powder, paprika, and cumin to the slow cooker. Season to taste with salt and pepper (I usually add 1 teaspoon fine sea salt and 1/2 teaspoon pepper; add to taste preference). Add chicken stock or broth.
COOK: Stir well. Cover and cook on high for 3-5 hours or low for 4-6 hours-- or until the chicken shreds easily.
SHRED CHICKEN: Remove the chicken and shred with two forks. While shredding the chicken, add in the freshly grated (if you use cheese from a bag it gets greasy) cheese and the half and half.
FINISHING CHOWDER: Return the shredded chicken and mix it into the soup. Taste and season to taste with salt and pepper; the flavors should sing!
SERVE: The toppings seal the deal! Ladle soup into bowls and top with desired toppings: additional handful of cheese, a few squeezes of fresh lime, finely chopped fresh cilantro, squirt of hot sauce, spoonful of sour cream, and/or diced fresh avocado.
INSTANT POT: Thanks Tammy for sharing how you make this in the Pressure Cooker! Tammy writes, "I make this all the time in my instant pot! I add everything but the cream and cheese. Then I choose soup and it cooks for 30 minutes. Shred the chicken and add the cream and cheese. We love this soup!"
STORAGE: Leftover chowder will keep well in the fridge, in an airtight container, for up to 5 days. Reheat in a pot over low heat, stirring frequently, until heated through. Don't boil the chowder or reheat it at a high temperature; this can cause the ingredients to separate or curdle. Because of all of the dairy in this chowder, it isn't a great candidate for freezing and thawing. The milk solids will separate as the chowder thaws, resulting in a grainy texture with some separation.