Wash and slice the zucchini into thin strips. Sauté them for 10 minutes over high heat in a little olive oil with salt, pepper, and chopped parsley, stirring regularly. Set aside.

Preheat the oven to 375°F (190°C).

Brush the bottom of your baking dish with olive oil. Layer the phyllo sheets in the dish, brushing the top sheet with olive oil as well. Bake for 2-3 minutes (no longer, or they may dry out).

Spread the yogurt over the phyllo sheets. Season with salt and pepper. Arrange the zucchini slices on top. Add the goat cheese and sprinkle with oregano. Bake again for 20-25 minutes.

If the edges brown too quickly, cover them with a sheet of aluminum foil.