Sauté the Aromatics: In a large Dutch oven or heavy-bottomed pot, melt the butter over medium heat. Add the diced onion and celery. Cook, stirring occasionally, until the vegetables are softened and translucent, about 5 to 7 minutes. Add the minced garlic and cook for 1 more minute until fragrant, being careful not to burn the garlic.

Make the Roux: Sprinkle the flour over the cooked vegetables. Stir continuously for 1 to 2 minutes. This step cooks the raw taste out of the flour and creates the foundation for the chowder’s thickness (a roux).

Whisk in Broth and Cook Potatoes: Gradually pour the chicken broth into the pot, whisking constantly to ensure the flour mixture is fully incorporated and no lumps remain. Once the mixture is smooth, add the diced potatoes and the dried thyme. Bring the mixture to a simmer.

Simmer and Soften: Reduce the heat to low-medium and let the chowder simmer gently, uncovered, for 10 to 12 minutes, or until the potatoes are fork-tender. Stir occasionally to prevent sticking to the bottom of the pot.

Add Ham and Corn: Stir in the diced cooked ham and the drained corn (or frozen corn). Continue to simmer for an additional 3 minutes, allowing the ham and corn to fully heat through.

Incorporate Dairy: Pour the whole milk (or half-and-half) into the soup base. Stir well to combine. Heat the chowder gently over low heat until it is hot and steaming. Crucially, do not allow the chowder to come to a full boil after adding the milk, as this can cause the milk to curdle or separate.

Season and Serve: Remove the chowder from the heat. Taste the soup and season with salt and fresh cracked black pepper. If the ham was very salty, you may need less added salt. Ladle the chowder into bowls and garnish with fresh parsley or chives, if desired, before serving hot.