Melt butter in a large saucepan over medium heat; cook and stir carrot, celery, onion, and garlic into hot butter until slightly softened, about 2 minutes. Stir flour into mixture to make a paste; cook until lightly browned and flour gives off a slightly toasted smell, about 5 minutes. Watch carefully, flour burns easily. Remove saucepan from heat and set aside to cool, about 15 minutes.
Stir white and yellow corn, potatoes, chicken, and 3 cups of chicken stock in a large soup pot over medium heat. Whisk remaining 1 cup chicken stock into vegetables and flour mixture until thoroughly combined. Stir mixture into ingredients in soup pot. Bring to a simmer, stirring constantly, until thick, about 5 minutes.
Stir half-and-half, nutmeg, salt, and black pepper into chowder. Bring back to a boil, reduce heat to low, and simmer until potatoes are tender, about 20 minutes.
I used precooked rotisserie chicken and just shredded the breast meat (and saved the rest for a later recipe) to save time, but you are more than welcome to cook your own meat and then shred it. You can even precook your potatoes to speed up the recipe. If you’re going to do this in a slow cooker, follow the directions above, just throw it in the cooker and cook on Medium for 5 hours.
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