In a large bowl, cover the cobs completely with cold water and let them soak for about 20-30 minutes-- but only if you want to add extra moisture to the corn; otherwise, skip this step. Shake off excess water from the cobs, if you have soaked them.
Then, heat the griddle pan over medium-high heat. Sprinkle a small amount of water onto the pan. The water will sizzle and evaporate quickly when griddle is hot enough. Then, tear 4 rectangular sheets of aluminum foil. Place one cob in the center of each sheet of aluminum foil.
Then, brush each cob with olive oil, and season with salt, pepper, and nutmeg. Wrap the aluminum foil around each ear of corn and enclose by twisting the ends tightly. Next, place wrapped cobs directly on the hot griddle pan and cook for about 20-25 minutes, turning the corn with tongs every so often.
Using oven mitts, remove from heat and open foil carefully. It will be super hot!!! Press on a few of the kernels. If liquid comes out, the corn is done. If you want the corn to have grilled marks, place unwrapped cobs directly on the griddle and let cook for about 3 minutes, turning occasionally.
Serve the grilled corn either simply, spread with butter, or topped with the Aioli and Parmesan cheese.