Place a small ovenproof frying pan over medium heat, to start heating the pan.
Trim and chop the scallion, and thinly slice the zucchini.
Melt the butter in the pan. Add the scallion and stir. Add the zucchini, in an even layer.
Beat eggs in a small bowl. When the zucchini is tender, pour the beaten egg over it in the pan. Let it cook undisturbed until the bottom is set.
Optional step: Use a spatula to loosen the edges, and let the uncooked egg run under the cooked layer, to speed up the process. Let that cook until set.
Slice the cheese. When the egg is mostly cooked, but the top is still runny, place the cheese over it and put the pan under the broiler. Let cook 2-3 minutes, until cheese is melted and egg is fully cooked to your liking.
Frittata can be served hot, warm, or even room temperature.