Place grated squash and 1 teaspoon salt in a colander and drain for about 20 minutes. Press squash to drain as much water as possible. Spoon squash to a clean, dry towel and squeeze to remove even more water.
In a medium bowl, combine squash and 1/2 teaspoon salt, green onions, flours, pepper, eggs and cheese. Stir to combine.
Heat oil in cast iron skillet. Scoop about 1/4 cup of batter at a time and release in skillet to form fritters; flatten slightly. Cook about 2 to 3 minutes on one side; flip and cook another 2 to 3 minutes or until nicely browned.
Serve these fritters with full-fat Greek yogurt and fresh chives. They make a great vegetarian main dish or a hearty vegetable side dish. They are also kid friendly and a great alternative for potato pancakes! If you are lucky enough to have any leftover fritters, try making Eggs Benedict with them, replacing the English muffin with a fritter or two.