1. Place potatoes, turnips, parsnip, and garlic in a medium saucepan; add enough half-and-half to cover. Place over medium high heat and cook until vegetables are easily pierced with the tip of a knife, 10 to 15 minutes. Drain, reserving cooking liquid.

2. Return vegetables to saucepan and add egg, butter, and 1/4 cup cooking liquid. Using a potato masher, mash until smooth, adding more cooking liquid as necessary. Season with nutmeg, salt, and pepper and serve immediately.