Beat the eggs in a medium-sized bowl with the salt.

Heat 1/2 tablespoon of oil in a large nonstick skillet over medium-high heat until hot. Add the beaten eggs. When the bottom is just set, scramble the eggs until they are mostly cooked but the inside is still a bit runny.

Add the remaining 1/2 tablespoon oil and the kimchi. Stir and cook until the kimchi is toasted and not watery anymore, 1 to 2 minutes.

Add the zucchini. Stir and cook until the zucchini is very lightly cooked, 1 to 2 minutes (*Footnote 1). Transfer everything to a big plate to cool.

Place the tortilla in a large skillet. Spread half of the cheese into a thin layer over the whole tortilla. Add half of the kimchi-zucchini stir fry over the cheese, then add half of the eggs between the gaps of the vegetables. Sprinkle half of the green onion. Aim to have everything spread out evenly without too much overlap, so they are all in contact with the cheese.

Heat up the skillet over medium heat. Cook until the cheese is melted completely, 2 to 3 minutes. Carefully use a spatula to lift one side of the tortilla and fold it over onto the other side, to form a half moon. Once the cheese melts, the toppings will stick to it and stay put during the folding.

Slide the quesadilla onto a cutting board. Use a sharp knife to cut it into three or four even wedges. Make the other quesadilla using the same method.

Garnish the quesadilla with cilantro. Serve hot with your favorite salsa, hot sauce, and / or sour cream.