Preheat oven to 350 degrees F.
In a large bowl, stir together corn, bell pepper, cornmeal, sugar, salt, baking powder, and egg yolks. In a separate bowl, using an electric mixer, beat egg whites until stiff peaks form. Fold whites into cornmeal mixture.
In a large skillet, heat 2 tablespoons oil over medium heat.
Working in batches, drop half the batter by scant 1/4-cup mounds into the oil, flattening them slightly with a spatula, and cook for 2 minutes per side, or until golden brown. Transfer to a baking sheet and repeat with remaining batter and 2 tablespoons oil.
Divide Cheddar evenly among corn cakes and bake for 1 minute, just until cheese has melted. Remove from oven, and make 4 stacks of 3 cakes each. Top stacks evenly with arugula. Serve immediately.
