Preheat oven to 375°F.
In small bowl, combine grated cheese, garlic powder, paprika, salt, and pepper, stirring with fork until mixed.
Pour olive oil into a glass baking dish. Tilt dish around until olive oil evenly coats entire bottom.
Evenly sprinkle the cheese mixture over bottom of pan (don't dump it in and then try to spread it out. Once it touches the olive oil, it becomes almost impossible to spread the cheese out evenly--it will clump. It works better to sprinkle slowly and evenly over the entire surface).
Arrange the potatoes in a single layer, cut side down, on top of cheese mixture. Press down to ensure potatoes are flat and in contact with cheese layer. Sprinkle thyme over top and season with salt.
Bake for about 30 minutes, or until cheese is browned and potatoes are soft when pierced with fork. Remove from oven and leave potatoes to rest in pan for 5 minutes. Remove potatoes from pan using a small spatula, being careful to keep the cheese layer intact on the cut side of the potato. (Use a paring knife to cut cheese between the potatoes, if necessary.)