Prepare Batter: In a mixing bowl, combine the all-purpose flour, water, egg, salt, and black pepper. Whisk until smooth and slightly thick, about 2-3 minutes.

Add Vegetables: Gently fold in the green onions, carrot, and zucchini. Mix until evenly distributed, about 1-2 minutes.

Heat Oil: Add enough vegetable oil to coat the skillet bottom and heat over medium until shimmering, about 3-4 minutes.

Cook Pancakes: Pour a ladleful of batter into the hot oil. Cook for 3-4 minutes until golden brown at the edges, then flip and cook the other side for another 3-4 minutes.

Drain Excess Oil: Transfer cooked pancakes to a plate lined with paper towels for 1-2 minutes to drain.

Repeat: Continue cooking the remaining batter, adjusting oil as necessary, for a total of about 20-25 minutes.

Serve: Enjoy warm with a dipping sauce or pickled vegetables.