In a large, heavy-bottomed pot or Dutch oven, melt the 2 tablespoons of unsalted butter over medium heat. Add the diced onion and diced celery. Sauté gently for 5 to 7 minutes, stirring occasionally, until the vegetables have softened and the onion is translucent. Add the minced garlic and cook for 1 minute more until fragrant.

Sprinkle the 1/4 cup of all-purpose flour over the sautéed vegetables. Stir continuously with a wooden spoon or whisk for 1 to 2 minutes. This creates a roux (a fat and flour mixture) which will thicken the chowder. Ensure the flour cooks slightly to remove the raw taste.

Slowly pour in the 4 cups of chicken broth, whisking constantly as you pour to prevent the formation of lumps. Once all the broth is added and the mixture is smooth, add the diced Russet potatoes, the 1/2 teaspoon of dried thyme, and the 1/4 teaspoon of black pepper.

Bring the mixture to a boil over medium-high heat, stirring frequently. Once boiling, immediately reduce the heat to low, cover the pot slightly, and allow the chowder base to simmer for 10 to 15 minutes, or until the potatoes are completely fork-tender.

Once the potatoes are cooked, stir in the 2 cups of diced cooked ham and the drained corn. Pour in the 1 cup of whole milk or half-and-half. Stir well and increase the heat back to medium-low.

Heat the chowder until it is steaming hot, stirring frequently, but do not allow it to come back to a rolling boil once the dairy is added, as this can cause the milk to curdle. This heating process usually takes about 5 minutes. Taste the chowder and adjust the salt levels as necessary (remember that the ham contributes significant salt).

Ladle the Easy Ham and Corn Chowder into bowls. Serve immediately, garnished with fresh parsley or chives if desired.