- Add water and cubed potatoes to stockpot. Bring to a boil over medium-high heat.
- Reduce heat to medium and boil potatoes until tender, about 20 minutes.
- Remove potatoes with slotted spoon to bowl. Drain stockpot, reserving 1-cup potato water.
- Stir in butter, chopped onion, and all-purpose flour. Season with salt and pepper.
- Stir in potatoes, reserved liquid, whole milk, white sugar, cheddar cheese, and diced ham.
- Simmer 30 minutes, stirring frequently.