Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Pour a generous drizzle of olive oil over the parchment, spreading it evenly to create a smooth coating. Sprinkle a thick layer of grated Parmesan cheese across the oiled surface, ensuring full coverage. Add a light scattering of fresh thyme to infuse the cheese with aromatic flavor.

Arrange the potato halves cut side down directly over the Parmesan layer. Press each piece slightly so the flat surface makes firm contact with the cheese. This step helps create that crisp, golden crust as the potatoes bake.

Transfer the tray to the oven and bake for 20 to 30 minutes, or until the Parmesan forms a deep golden crust and the potatoes are tender inside. Remove from the oven and allow them to rest briefly before serving.

For an extra touch of richness, drizzle the potatoes with balsamic glaze or serve them as they are—each piece will lift easily from the sheet, revealing a beautifully crisped Parmesan bottom with a fragrant hint of thyme. Perfect as a side dish or a snack on its own.