Whisk eggs together in a large bowl until smooth. Stir in shredded and diced zucchini until well combined. Mix in basil, Parmesan cheese, salt, and pepper. Add flour a little at a time, stirring between additions until no dry lumps remain.

Heat oil in a large skillet to 375 degrees F (190 degrees C).

Drop batter spoonfuls of batter into oil, a few at a time; do not overcrowd the skillet. Cook until golden brown, about 4 minutes per side. Drain on a paper towel-lined plate before serving.