Mince 6 cloves of garlic and 1 onion (any color). Finely chop 4 stalks of celery.
Peel and slice 4-5 large carrots (yields 3-4 cups of chopped carrots). Feel free to chop the slices into halves or quarters if desired.
Peel 4-6 Russet (also known as Idaho) potatoes and cut them into chunks, making sure they are relatively equal in size to ensure even cooking (yields 5 heaping cups chopped potatoes).
Cut 1 lb. ham steak, quartered ham, or leftover ham into cubes.
Place a cast iron Dutch oven or heavy-bottomed soup pot on the stove top and heat to medium-high. Add 1 Tbsp. olive oil. Once heated (the ham should sizzle as it hits the oil), add the chopped ham to the soup pot and sauté for 5-6 minutes, stirring often. The ham should brown slightly and some of the fat should render. After the ham has sautéed, remove it from the pot and set aside.
Add 1 Tbsp. olive oil, along with the minced garlic, onions, and celery. Sauté for 5-7 minutes, stirring often. Add the chopped carrots, along with ½ tsp. each kosher salt and pepper. Sauté the carrots for 5-6 minutes, stirring often. Add 4 ½ cups of low sodium chicken broth and 1 tsp. of Italian seasoning to the pot. Stir until incorporated. Bring the soup to a boil. Once boiling, reduce the heat to a low boil, cover, and cook for 15 minutes. After 15 minutes, remove the cover, and add the diced potatoes and ham. Return the soup to a boil, reduce to a low boil, cover, and cook for another 8-10 minutes.
At the end of the cooking time, remove 1-2 cups of the diced potatoes and place them in a small bowl. Mash them with a fork or a potato masher. Return the mashed potatoes to the soup and stir until completely combined. Cook the soup for another 2 minutes. Once finished, remove the Dutch oven from the stove top, so that the potatoes do not overcook and become mushy.
To Serve: Serve with some freshly minced herbs like chives or parsley (optional).