Melt butter in a small saucepan. Sweat the carrots, onion and ginger with the butter. Add potatoes and broth, then bring to a boil. Reduce heat, and simmer until potatoes are tender. Strain liquid into a separate container. Put vegetables into a blender along with the dill, and pour in just enough of the liquid to cover the vegetables. Puree in stages if necessary. Discard excess broth. Return vegetable puree to pan.
Stir heavy cream into the pan with the vegetables. Season with salt and pepper. Heat, but do not boil, and serve immediately.