In a large saucepan, combine the cubed potatoes, chopped carrots, salt, and water.

Bring to a boil, then reduce heat and simmer, uncovered, until the vegetables are tender, about 10-15 minutes.

Drain and set aside.

Meanwhile, in a Dutch oven, melt the butter over medium heat.

Add the chopped onion and celery, and sauté until tender.

Stir in the all-purpose flour and pepper until blended.

Gradually pour in the whole milk, stirring constantly.

Bring to a boil, stirring occasionally, and cook until thickened, about 2 minutes.

Remove from heat and stir in the shredded cheddar cheese until melted.

Stir in the cubed fully cooked ham and the cooked potato mixture.

Heat through over low heat.