Shred the squash in your food processor using the shredding attachment or grate it by hand. Chop the onion finely. Place both in a colander and press on them repeatedly with the back of a spoon to eliminate as much liquid as possible.
In a medium bowl, whisk the egg with salt, black pepper, and garlic powder. Add the grated squash and chopped onion and mix to blend. See the notes section below about adding flour to make them sturdier.
Heat a large 12-inch nonstick skillet over medium heat. Brush the skillet with half of the butter. Measuring ¼ cup per fritter, spoon the mixture onto the skillet. Fry without moving for 4-5 minutes, until you can see that the bottoms are browned.
Carefully flip the fritters to the other side and fry them for 4-5 more minutes, until browned on both sides. Brush the skillet with more butter and repeat with the remaining squash mixture.
Serve immediately. You can top the fritters with a dollop of sour cream or salsa.
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Notes
Lacking the starch found in potatoes, these fritters are flimsy and delicate, so take great care when flipping them and when removing them from the skillet. The more water you remove from the squash and onion, the sturdier they will be.
You can add flour or Parmesan to make the fritters sturdier and less likely to fall apart. If you start making them and decide they are too watery/fragile, add 2 tablespoons of all-purpose flour (if you don’t mind the gluten and carbs), ¼ cup of superfine almond flour, or ¼ cup of grated Parmesan cheese to the remaining mixture.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. Reheat them uncovered in a 350°F oven. They are also good cold, straight out of the fridge!
To freeze the leftovers, place them on a wax-paper-lined tray in a single layer and freeze. Once frozen, you can place them in freezer bags. Thaw them overnight in the fridge before reheating them in a 350°F oven.