Place a large (10 inch wide) nonstick skillet that is oven safe on the stovetop. Heat over medium heat.
While heating, grate the zucchini using a coarse grate. You can also chop if you wish.
Add the oil to the skillet. When the oil is hot, add the zucchini and corn. Cook until the zucchini is just tender, approximately 3-5 minutes.
While the vegetables are cooking, in a small bowl, whisk together the eggs, cheese, salt, and black pepper.
When the zucchini is just tender, add the egg mixture to the skillet. Stir briefly. Let the egg mixture cook until the edges just begin to set, approximately 3-5 minutes.
Turn off the stove and place the oven safe skillet in the oven. Bake until the eggs are completely cooked through and the frittata is dry to the touch on top, approximately 10-12 minutes.
Remove the frittata from the oven. Run a rubber spatula around the edge of the frittata to loosen it and either slide it out or flip it onto a plate. Serve immediately.
Notes
To ensure a truly vegetarian frittata, make sure to use a vegetarian cheese.I use frozen corn, just make sure it is thawed before adding it to the oil. You can also use fresh corn or canned corn that has been drained.