Heat oven to 375° F. Spray an 8-inch or 9-inch square baking dish with nonstick spray. Set aside.
Whirl Parmesan, potato flakes and oregano in a small food processor until well mixed and resembling fine crumbs.
Brush chicken thighs lightly with olive oil. Place thighs in prepared baking dish. Top each thigh with a thick layer of the breading, using all of it.
Bake, uncovered, for 45 minutes. Remove from oven and serve.
[b]To use boneless, skinless thighs:[/b] Follow the recipe except the chicken amount will be about 1 ½ pounds of boneless, skinless thighs. Baking time will be 35-40 minutes.
[b]For a fancier presentation:[/b] Peel the papery skin off several large onions. Cutting through the equator of the onion, cut 3/8-inch thick slices and lay one slice/plank under each chicken thigh. Proceed with recipe using either bone-in or boneless thighs, placing each chicken thigh on onion plank, then piling the topping on as described above, and baking. To serve, slide a spatula under each chicken-onion parcel, keeping onion intact, and transfer to plate.