Preheat the oven to 350ºF (175ºC) and position an oven rack to the center position. Grease a 9x9-inch baking pan with butter.
In a medium mixing bowl, whisk together the sweet rice flour, baking powder, and salt. Set aside.
Place 2 1/2 cups of corn kernels and the coconut milk in the bowl of a high-speed blender. Blend until smooth, about 30 seconds. Set aside.
In a large mixing bowl, whisk together the eggs and sugar until smooth. Next, add the melted butter and whisk to combine. Pour in the corn and coconut milk mixture and whisk again.
Add the flour mixture to the bowl all at once. Using a wooden spoon, stir until you no longer see large lumps of flour. The batter should be relatively smooth.
Fold in 1/2 cup corn kernels, scallions, and parmesan cheese.
Pour the batter into the greased pan and use a spatula to spread it out to an even layer.
Bake the mochi for 55 to 60 minutes, rotating the pan after 30 minutes of baking. The mochi should be evenly golden brown at the top. When you gently press the center of the mochi with your fingers, it should bounce back slightly.
Let the mochi cool in the pan for 30 minutes before unmolding. You can start eating the mochi after 30 minutes of cooling or let it reach room temperature before serving. The center of the mochi is more gooey when it’s still warm. When it’s cooled completely, the edges develop a better crust and the mochi will be easier to cut. Cut the mochi into 16 or 20 pieces. I recommend cutting the mochi with a greased knife to get cleaner cuts. Pour a bit of oil onto a paper towel and use that paper towel to grease the blade of a knife. Wipe the blade with the greased paper towel after each cut.
Store any leftovers in a container at room temperature overnight. If you want to store the mochi for more than a day, refrigerate them for up to 4 days. The best way to reheat the leftovers is in the oven. Reheat the mochi on a baking pan at 350ºF (175ºC) for 8 to 9 if stored at room temperature, or 10 to 12 minutes if stored in the refrigerator. Let the mochi cool for 10 to 15 minutes before eating. I actually like the corn mochi best after it is reheated! (See note 3 for freezing directions.)