Melt butter in a large pot over medium heat. Cook onion for 4 minutes.

Add potatoes and broth. Bring to a boil, then simmer for 15 minutes, until tender.

Mash some potatoes in the pot, leaving a few chunks for texture.

Stir in ham, milk, cream, salt, and pepper. Warm for 5 minutes without boiling.

Taste and adjust the seasoning. I serve it with crackers because hungry kids rarely wait patiently.