In a large bowl, add the zucchinis, carrot, onion, eggs, tapioca flour, baking powder, and garlic powder. Season with salt and pepper and mix together well.

Heat a large nonstick skillet over medium heat. Drizzle enough olive oil int to the hot skillet to coat the bottom. Working in batches, scoop the batter into the skillet, ¼ cup per fritter, flattening it with the back of the measuring cup. Cook until golden brown on the bottom, 4 to 5 minutes. Flip the fritters over and cook until the second side is golden brown, 2 to 3 minutes. Transfer to a plate and immediately grate the lemon zest over them. Sprinkle with the sliced basil. Wipe the skillet clean and repeat with the remaining batter and garnishes. Serve warm.