Old-fashioned ham and potato soup.

The Simmer: In a large Dutch oven or heavy pot, combine the potatoes, carrots, celery, onion, and ham bone (if using). Cover with the chicken broth.
The Tenderness: Bring to a boil, then reduce heat to medium-low. Cover and simmer for 20–25 minutes until the potatoes are very soft. If you used a ham bone, remove it now and scrape off any extra meat into the pot.
The “Mash” (Texture Secret): Use a potato masher to lightly crush about 1/3 of the potatoes directly in the pot. This releases the starch and thickens the base naturally.
The Roux: In a separate small saucepan, melt the butter. Whisk in the flour and cook for 1 minute. Slowly whisk in the milk until smooth and slightly thickened.
The Combine: Pour the milk mixture and the diced ham into the large soup pot. Stir well.
The Final Season: Let the soup simmer for another 5–10 minutes. Stir in plenty of black pepper. Taste before adding salt—the ham usually provides enough!

The Ham Bone: If you have a leftover ham bone from a holiday dinner, use it. Simmering the bone with the potatoes extracts marrow and smoky flavor that pre-packaged diced ham simply can’t match.
Yukon vs. Russet: If you want a smoother soup, use Russets (they break down). If you want defined chunks that stay buttery, use Yukon Golds. A 50/50 mix is the “pro” move.
The “Cool Down” Thickening: This soup is always better 20 minutes after it’s done. As it cools slightly, the starches “set,” making it much creamier than when it’s boiling hot.