Melt 1 tablespoon butter in a large saucepan over medium heat. Add onion, and sauté 4 to 5 minutes or until soft. Stir in potato, carrot, and parsnips. Add water, and bring to a boil. Cover, reduce heat, and simmer 20 to 25 minutes or until vegetables are tender. Uncover and cook 8 to 10 minutes or until liquid evaporates, stirring occasionally.
Add broth and remaining 1 tablespoon butter. Mash mixture with a potato masher. Stir in chives, salt, and pepper.