Peel potatoes and cut them into 1/4" dice. Cut carrots into 1/4" dice. Coarsely chop scallions. Cut ham into 1/4" dice. Shred cabbage.
In a medium saucepan, melt butter over medium heat until hot but not smoking. Add potatoes, carrots and scallions and saute until scallions are wilted, about 5 minutes.
Stir in flour and cook, stirring, for 1 minute.
Add cabbage, water, broth, dill and pepper, and bring the mixture to a boil over medium-high heat. Reduce heat to medium-low, cover and simmer 20 minutes, stirring occasionally.
Just before serving, gently mash vegetables with a potato masher to thicken liquid if desired. Stir in the ham. .
(Notes: I don't mash the potatos because I prefer potato soup that way, and it is already pretty thick for me. I also have used chicken bullion and water to make the broth called for, and it has worked fine for me.).