Begin by dicing the carrots, celery, and onion into small, even pieces. Cube your potatoes into ½-inch chunks and cut the ham into bite-size pieces.

In a large pot, heat the olive oil over medium heat. Add the diced carrots, celery, and onion. Sauté for about 5 minutes until soft.

Add the cubed potatoes, vegetable broth, and prepared ham to the pot. Bring to a boil, then reduce to low and let simmer for 15 minutes.

In a separate saucepan, melt the butter over medium heat. Whisk in the flour to create a roux, then gradually pour in the milk, whisking constantly until thickened.

Stir in the pepper and garlic powder into the soup mixture. Gradually add the roux while stirring. Cook for an additional 10 minutes.

Adjust salt if necessary, and stir in the parsley. Serve hot.