Place peeled turnips in a pot of salted water to cover. Bring to a boil.
Cook for 20-30 minutes or until the turnips can be pierced easily with a paring knife.
Drain well. Let cool slightly. (You can also do them in an Instant Pot, but you’ll have less control over the doneness. See Instant Pot instructions below.)
Preheat oven to 375 degrees. Place the turnips on a clean kitchen towel or a 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 can drain and dry a bit.
Combine the 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. (If using foil, spray it with a light coating of cooking spray.) Place the flattened turnips on the lined baking sheet. Brush each turnip with a little of the olive oil-garlic mixture.
Sprinkle the Parmesan cheese over each turnip, gently pressing it down. Quickly and decisively flip each turnip over. Repeat with the remaining olive oil, garlic, and cheese on the other side.
Bake for 20-25 minutes. Flip each turnip and bake for an additional 15 minutes.
Garnish with chopped fresh chives if desired and serve.