1-First Step: Build the soup base In a large stockpot, combine the potatoes, celery, carrots, chopped onion, diced and cooked ham, and ham stock or broth. Bring the pot to a gentle boil over medium-high heat. Once boiling, reduce heat to medium and simmer until the potatoes are tender when pierced with a fork, about 12 to 15 minutes depending on cube size.

2-Second Step: Season the broth After the potatoes are tender, stir in 2 tablespoons chicken bouillon if you are not using a rich chicken broth, plus salt to taste and 1 teaspoon pepper. Taste the liquid and adjust seasoning. Remember that the ham and cheese add salt, so err on the light side with added salt.

3-Third Step: Make the roux and cheese sauce In a separate saucepan, melt 5 tablespoons butter over medium-low heat. Whisk in 5 tablespoons flour and cook, stirring constantly, for about 1 to 2 minutes until the mixture is bubbling and smells slightly toasty but not browned. This cooks out the raw flour taste. Gradually whisk in 2 cups milk to prevent lumps, adding a little at a time while whisking. Increase heat to medium and continue stirring until the sauce thickens, about 4 to 5 minutes. The sauce should coat the back of a spoon. Remove the sauce from heat and stir in 2 cups shredded cheese until fully melted and smooth. Return to low heat only if you need to melt a few remaining shreds, but avoid boiling the sauce once cheese is added.

4-Fourth Step: Combine and finish Stir the cheese sauce into the stockpot with the tender potatoes and vegetables. Heat through over low to medium heat until the whole pot is steaming and cohesive, about 3 to 5 minutes. For a thicker texture, mash some of the potatoes right in the pot with a potato masher or hold back 1 cup of cooked potatoes, mash them, and return them to the pot slowly.

5-Final Step: Adjust and serve Give the soup a final taste and adjust salt and pepper. If the soup becomes too thick as it cools, thin with a splash of milk or broth. Serve hot with chopped green onions, crispy bacon bits, or crusty bread. The soup will thicken as it cools, so serve while warm for the best texture.