In a large saucepan, heat butter over medium-high heat; saute leeks and chives until tender. Stir in mashed potatoes, savory and broth; bring to a boil. Reduce heat; simmer, uncovered, until flavors are blended, 8-10 minutes.
Puree soup using an immersion blender or cool slightly and puree soup in batches in a blender; return to pan. Stir in cream, salt and pepper; heat through.