Add the cornmeal, baking powder, salt, egg, and water to a bowl and stir to combine. Once mixed, stir in the corn. The mixture should be the consistency of pancake batter.
For stovetop cooking: Place a cast iron griddle over medium heat. Brush with oil and heat until shimmering. Pour enough batter (about 2 tablespoons) onto the griddle to form a 4-inch round. (Depending on the size of your griddle, you can cook more than one cake at a time.) Cook until brown on both sides, 2 to 3 minutes per side. Serve immediately or transfer to a warm (200°F) oven until all of the cakes are done.
For cooking outdoors: Heat coals in a chimney starter until hot and ashy. Using an outdoor Dutch oven with feet, turn the oven upside down. Place 22 hot, ashy coals on the bottom of the inverted oven. Lay the lid upside-down on top of the Dutch oven feet and over the coals and let heat for 10 minutes.
Brush the lid with oil and heat until shimmering. Pour enough batter onto the lid to form a 4-inch round, approximately 2 tablespoons. (Depending on the size of your lid, you can cook more than one cake at a time.) Cook until brown on both sides, 2 to 3 minutes per side. Serve immediately.