Rinse the box grater under water, but you don’t have to thoroughly clean it. Just get the flecks of cucumber off. Dry it, then snip the end off the squash. Grate them on the large holes of the box grater as you did the cucumber. Place the shreds in a cheesecloth or paper towels and squeeze to wring mostly dry. Add to a large mixing bowl, along with beaten egg, flour, baking powder, Parmesan, basil, garlic powder, salt, and pepper. Mix together until a uniform batter forms.
Pour oil into a large skillet. You want it to come up around ½ an inch up the sides - you’re looking for not enough oil to deep fry, but a little more than a simple pan fry. Heat over medium-high heat until it registers 350℉ on a candy thermometer. If you don’t have one, you can test with a drop of batter. It should sizzle right away but not immediately brown.
Once the oil is ready, add the batter in whatever size spoonful you like. I just used a cereal spoon. Use the back of the spoon to flatten and if you want, shape the fritters into circles. You can see I don’t really mess with that kind of thing, I let the fritters be themselves. You can cook the fritters in batches, but space them at least one inch apart. You’ll likely need two to three batches to cook them all.
Let them go 3 to 4 minutes per side. Use a slotted spatula to transfer them to a paper towel lined plate. Serve immediately with the Cucumber Tzatziki.