Grate zucchini using a box grater, sprinkle lightly with salt, and let sit for 10 minutes.
Transfer zucchini to a clean kitchen towel and squeeze out as much liquid as possible.
In a bowl, mix drained zucchini, egg, mozzarella, Parmesan, garlic powder, and black pepper until combined.
Preheat oven to 400°F (205°C) and line a baking sheet with parchment paper.
Divide mixture into 4 portions and flatten into rectangular slices about ¼-inch thick.
Bake for 15 minutes, flip carefully, then bake another 10–12 minutes until firm and lightly golden.
Mix melted butter with minced garlic and parsley if using.
Brush one side of each zucchini slice with garlic butter.
Place cheese slices and optional fillings on the unbuttered side of two zucchini slices.
Top with remaining zucchini slices, garlic-butter side facing out, and press gently.
Heat a nonstick skillet over medium heat and cook sandwiches 2–3 minutes per side until golden and cheese melts
or return to oven and bake at 400°F for 8–10 minutes, flipping once.
Let rest 1–2 minutes before serving.