Melt butter in a large saucepan over medium heat; cook and stir onion, carrot, celery, and garlic in 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 as flour burns easily. Remove saucepan from heat and set aside to cool slightly.

Meanwhile, stir together potatoes, chicken, white and yellow corn, and 3 cups stock in a large soup pot over medium heat.

Whisk remaining 1 cup stock into vegetables and flour mixture until thoroughly combined. Stir mixture into the soup pot; bring to a simmer. Cook and stir until thick, about 5 minutes.

Stir half-and-half, nutmeg, salt, and black pepper into chowder. Bring to a boil, reduce heat to low, and simmer until potatoes are tender, about 20 minutes.