1. Place turnips, potatoes, and garlic in a 5-quart pot. Cover with cold water to 2 inches above the vegetables; bring to a boil. Add salt; simmer, uncovered, until tender (about 15 minutes).
2. Drain the vegetables in a colander; return to pot. Cook over medium heat to remove excess water, stirring well (about 5 minutes). Stir in the remaining ingredients; mash with a potato masher until smooth. Transfer mixture to a serving dish.