Wash and dice the potatoes, celery, carrots, and onion into bite-sized pieces. Mince the garlic and prepare cooked chicken.

Melt butter in a large stockpot over medium heat. Add onion, celery, carrots, and garlic. Sauté for 5-7 minutes until softened.

Pour chicken broth, parsley, salt, and pepper into the pot. Add diced potatoes, bring to a simmer, and cook for 15-20 minutes.

Whisk milk and flour together until smooth. Gradually stir this into the soup along with cooked chicken. Cook for another 5 minutes.

Lower heat and add Velveeta cheese, stirring until melted and combined.

Ladle chowder into bowls, garnish with additional cheese and parsley. Serve warm.