Place grated zucchini in a sieve or colander, sprinkle with 1/2 teaspoon salt and place over a large bowl. Let stand 15 minutes. Press out excess liquid until you can't get any more. (I put the zucchini in a thin kitchen towel to squeeze out the liquid.) Place zucchini in a dry bowl.
To the zucchini, add the beaten egg and egg yolk, 1/2 cup flour, Parmesan cheese, and 1/2 teaspoon salt. Mix in parsley, corn, green onion, yellow onion, green and/or red peppers, basil and/or garlic (both of which are optional) and stir until combined. If batter is still very wet, add more flour 1 spoonful at a time. If batter needs more moisture, add the reserved egg white.
Heat 4 tablespoons of olive oil in a large skillet over medium heat. Working in batches, drop by heaping tablespoons (or to the size you want) into the skillet and flatten a bit with the back of the spoon. Fry until golden, about 5 minutes on each side, adding more olive oil as needed. Transfer to paper towels and sprinkle with a little more salt to taste and freshly ground black pepper.
For an extra zing, I top mine with a dollop of chipotle-lime-mayo which I make by adding 2 teaspoons chipotle juice or 1 chopped chipotle to 2 tablespoons mayo and the juice of 1/2 of a lime. But be sure and add the chipotle in small portions so you can adjust to your personal taste...I like things zippy. You can buy a small can of chipotle and refrigerate the leftovers in a plastic container for several months. You could also just use a dollop of sour cream.