Place the shredded zucchini in a colander in the sink. Sprinkle with 1/2 teaspoon salt and let sit for 5 to 10 minutes so water can strain. Use a paper towel or cheese cloth to squeeze out any extra water.
Place the zucchini in a bowl. Add the flour, eggs, green onions, and remaining 1/2 teaspoon salt. Stir just until combined.
Add the olive oil to a large skillet and heat over medium-low heat. After a minute, scoop the mixture with a large cookie scoop (or 3 Tablespoons) and add to the pan. Gently press down with a spatula and then cook 2 to 3 minutes, or until golden brown. Flip and then cook an additional 2 to 3 minutes. Turn up the heat or turn down if browning too fast.
Transfer cooked zucchini fritters to a plate lined with paper towel. Sprinkle the top with salt and pepper if desired. Serve the zucchini fritters with sour cream and chives if desired.
Variation: If you want to boost the flavor ad in a clove of minced garlic and a couple Tablespoons of grated parmesan cheese.