Preheat the oven to 375°F (190°C).
In a mixing bowl, whisk together the eggs, milk, salt, and black pepper.
Stir in the corn kernels and shredded cheddar cheese.
Heat the olive oil in an oven-safe skillet over medium heat.
Pour the egg mixture into the skillet and cook until the edges start to set, about 5 minutes.
Transfer the skillet to the preheated oven and bake until the frittata is fully set and lightly golden, about 15 minutes.
Remove from the oven, let cool slightly, slice, and serve warm.