Place the vegetables, basil, salt, garlic powder and egg in a food processor and pulse until finely chopped and mixed. Add the flour and pulse a couple of times, just until combined.
Lightly coat a large skillet with oil and heat over medium heat. Place 1-tablespoon dollops of the batter in the skillet and cook until golden, 1 to 2 minutes per side. Transfer to plates and repeat with the remaining batter, adding more oil as needed between each batch.