Coarsely grate the zucchini and place in a colander in the sink. Sprinkle with salt, and allow to drain for 30 minutes. Press to remove excess water, then pat dry with paper towels until damp but not dripping.
In a medium bowl, combine zucchini, breadcrumbs, cornmeal, and Parmesan. In a small bowl, combine egg, mayonnaise, and seasonings. Add egg mixture to zucchini mixture and combine.
Portion the zucchini mixture into even amounts, shaping into a ball, then lightly pressing down to form a cake. Place the cakes on a piece of parchment paper until ready to cook.
Drizzle olive oil in a non-stick skillet over medium-low heat. Gently transfer the cakes to the skillet using a spatula. Turn after a few moments, then turn again, until they are golden brown and crispy.
Serve while hot with lemon wedges and condiment of your choice based on seasoning, such as salsa, tapenade, sour cream, or tartar sauce.
Uncooked cakes can be wrapped and stored in the fridge for up to 24 hours.