01 - Heat olive oil in a large pot over medium heat. Add onion, celery, and carrots. Sauté for 5 minutes until vegetables begin to soften.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown the garlic.
03 - Add diced ham and potatoes to the pot. Cook for 2 minutes, stirring occasionally to distribute evenly.
04 - Sprinkle flour over the mixture while stirring constantly to coat all ingredients evenly and prevent lumps from forming.
05 - Gradually pour in chicken broth while stirring continuously. Add thyme, salt, and pepper. Bring the mixture to a gentle boil.
06 - Reduce heat to low, cover pot, and simmer for 15 minutes until potatoes are fork-tender when pierced with a knife.
07 - Stir in milk and fat-free half-and-half. Heat through for 3 to 5 minutes, stirring frequently. Do not allow the soup to reach a boil as dairy may separate.
08 - Taste the chowder and adjust salt and pepper as needed to suit personal preference.
09 - Ladle hot chowder into serving bowls. Sprinkle with fresh chopped parsley and serve immediately.