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Heat the olive oil in a medium skillet over medium heat; add the onion and cook until it starts to soften, about 5 minutes, stirring occasionally. Add the zucchini and cook until softened and the water has evaporated, about 8 minutes, stirring occasionally; add the garlic and cook 1 minute more, stirring constantly. Cool slightly.
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Lightly beat together the eggs, flour, parsley, and black pepper in a medium bowl. Stir in the zucchini mixture.
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Add enough canola oil to a large nonstick skillet to lightly coat the bottom; heat the oil over medium heat.
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Drop the batter into the hot pan using a small (about 2 tablespoon) or large (about 4 tablespoon) scoop. Fry until set and golden on one side, about 2 minutes; flip and cook until set and golden on the other side, about 1 minute.
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Transfer the cooked fritters to a paper towel-lined plate to drain any excess oil, and cook the remaining egg mixture the same way, adding more oil to the skillet as necessary.