Place peeled turnips in a pot of salted water to cover. Bring to a boil. Cook 20 to 30 minutes or until turnips can be pierced easily with a paring knife. Drain. Let cool slightly.
Preheat oven to 375 degrees.
Place the turnips on a clean kitchen towel or double layer of paper towels. Gently press each one down until it's approximately 1/2-inch high. Let them drain for 15 minutes then carefully flip them over onto a dry section of the towel or onto fresh paper towels so the other side drains and dries a bit.
Combine garlic, olive oil and salt and black pepper, to taste in a small bowl.
Line a baking sheet with parchment paper or nonstick aluminum foil. Place the flattened turnips on the lined baking sheet. Brush each turnip with a little of the olive oil and garlic combination. Sprinkle Parmesan cheese over each turnip, gently pressing it down.
Carefully and quickly flip each turnip over. Repeat with the remaining olive oil and garlic combination and cheese.
Bake for 20 to 25 minutes. Flip each turnip and bake an additional 15 minutes. Garnish with chopped fresh chives and serve.