Place zucchini slices on a large plate; sprinkle 1 teaspoon salt on top. Let stand for 5 to 10 minutes. Drain off excess moisture and pat zucchini dry.
Beat remaining 1/4 teaspoon salt and eggs together in a small bowl.
Coat zucchini slices with flour and dip into beaten eggs.
Heat a nonstick skillet over medium heat. Cook zucchini until bottom is golden brown, about 5 minutes. Reduce heat to medium-low and flip; press down lightly and cook until second side is golden brown, about 5 minutes more. Transfer to a plate lined with paper towels. Let cool for 1 minute.
Whisk green onions, soy sauce, sesame oil, vinegar, sesame seeds, and red pepper powder together in a bowl to make dipping sauce. Serve zucchini with dipping sauce.