Heat stock into a large pot set over medium heat to a simmer. Stir in ham and 2 tablespoons rosemary.

Cook bacon in a large skillet over medium heat, turning occasionally, until crisp. Transfer bacon, using a slotted spoon, to pot. Discard half the bacon grease, reserve remaining grease in skillet. Return skillet to medium heat. Stir in green onions, leeks, onions, and garlic; cook until tender, then add to pot.

Add potatoes, carrots, and remaining 2 tablespoons rosemary to pot; simmer until vegetables tender, about 20 minutes. Off heat, stir in cream.