Prepare the zucchini
Grate the zucchini using a box grater to create fine shreds. Place the grated zucchini in a cheesecloth or kitchen towel and squeeze out as much moisture as possible.

Make the zucchini mixture
In a mixing bowl, combine the drained zucchini, beaten egg, grated Parmesan cheese, cornstarch, salt, and pepper. Mix well until a thick, dough-like consistency forms.

Cook the zucchini patties
Heat the garlic butter in a nonstick skillet over medium heat. Scoop the zucchini mixture into the skillet and shape it into two evenly sized patties.

Brown the patties
Cook each patty for 3–4 minutes until golden brown and crisp, then carefully flip.

Add the cheese filling
Sprinkle the shredded cheddar cheese over one patty. Place the second patty on top to form a sandwich.

Melt the cheese
Reduce heat slightly and cook for another 3 minutes, gently pressing the sandwich to help the cheese melt and bind the layers.

Rest and serve
Remove from the skillet and let it sit for about 1 minute before slicing. Serve hot.