01 - Heat olive oil in a large pot over medium heat. Add onion, celery, and carrots. Sauté for 5 minutes until vegetables are softened.
02 - Add garlic and cook for 1 minute until fragrant.
03 - Stir in diced ham and potatoes. Cook for 2 minutes, stirring occasionally.
04 - Sprinkle flour over mixture and stir well to coat vegetables and ham evenly.
05 - Gradually pour in chicken broth while stirring to avoid lumps. Add thyme, salt, and pepper. Bring to a gentle boil.
06 - Reduce heat, cover, and simmer for 15 minutes until potatoes are fork-tender.
07 - Stir in milk and half-and-half. Allow chowder to heat through for 3-5 minutes without boiling, stirring often.
08 - Taste and adjust seasonings as needed. Ladle into bowls, garnish with fresh parsley, and serve hot.