Using a sturdy vegetable peeler remove the thick skin from the turnips. Using a large knife, cut the turnips into 1½-inch square pieces. Place the turnips and garlic in a large pot and add enough lighty salted water to cover. Cover tightly, and bring to a boil over high heat. Uncover and reduce heat to medium-low. Boil gently for 20 minutes

Add the onion and continue cooking until the turnips are tender when pierced with the tip of a small sharp knife, 15 or 20 minutes more. Drain well and return to the warm cooking pot.

Add the Parmesan cheese, butter, salt and pepper. Using a large masher or an electric hand mixer, mash the turnips, gradually adding enough milk to reach the desired consistancy. Transfer to a warm serving dish.

Serve hot.

Note: The mashed turnips can be kept warm in a 170˚F oven, loosely covered with aluminum foil for up to 20 minutes.