Start by prepping your veggies. Chop the onion and celery finely—they’re the base flavor. Next, peel and cube those potatoes. Aim for even-sized pieces to ensure uniform cooking. Gather all the ingredients. Trust me, having everything ready makes the cooking process smoother and more enjoyable.

In a large pot, melt 5 tablespoons of unsalted butter over medium heat. Add the diced onion and celery. Sauté until they become translucent, about 4 minutes. It's amazing how such simple ingredients can build the foundation for the soup's flavor, don’t you think?

Add the 5 tablespoons of all-purpose flour to the pot. Stir well, ensuring there are no lumps. This mixture, your roux, needs to cook for about 2 minutes—it helps the soup thicken later. The smell of sautéed onions and flour alone is tantalizing.

Toss in your cubed potatoes. Now’s the time to fold in your 2 tablespoons of chicken bouillon powder. Mix with enthusiasm, letting the flavors mingle.

Next, pour in 3 ¼ cups of water and 2 cups of whole milk. Bring it all to a boil, then reduce to a gentle simmer. At this stage, it’s essential to keep an eye on it, stirring occasionally. You want to prevent the bottom from sticking while the potatoes transform into a soft, comforting bite.

After about 15-20 minutes of simmering, when the potatoes are fork-tender, add the ¾ cup of diced pre-cooked ham. Don’t forget to sprinkle in 1 teaspoon of ground white or black pepper and ½ teaspoon of salt to taste. Just imagine that blend!

Let everything merge together for another 5 minutes. Finally, add ¼ cup of grated Parmesan cheese and 1 tablespoon of fresh thyme leaves.

Stir until the cheese is all melty and incorporated. The result should be a creamy, thick broth. Just like that, you’ve got ham and potato soup ready!