Preheat the oven to 350°. Crack the eggs into a medium bowl and beat well to mix, then beat in the coarsely chopped cilantro.
In an 8-inch nonstick ovenproof skillet, heat 1 teaspoon of the olive oil. Add the corn kernels and sauté for 2 minutes. Add the sliced shiitake, season with salt and pepper and cook, stirring, until the vegetables are softened but not browned, about 5 minutes.
Add the remaining 2 tablespoons of olive oil to the skillet and heat. Add salt and pepper to the eggs and pour them into the skillet. Stir lightly to combine the ingredients, then transfer to the oven. Bake for 6 to 7 minutes, or until just set. Shake the skillet over high heat to loosen the frittata, then slide it onto a serving plate. Sprinkle with the Parmesan, cut into wedges and serve.