Shred zucchini (about 2 cups) and carrots (about 2 cups).

Combine zucchini, carrots, and corn in a large bowl.

Add the egg, yogurt, salt, and pepper and stir.

In a separate bowl, combine the flour, cornmeal, and baking powder. Add it to the veggies. Fold in the shredded cheese.

Heat olive oil in a skillet.  Form balls of dough and press into a patty, using about 1/8 cup of dough.   Add to skillet and cook on both sides (pressing to flat with  the back of your spatula so it gets hot and cooked throughout the pancake).