Preheat the oven to 350°F.
Place the zucchini coins and the oil in a large ziplock bag. Shake it up until the zucchini coins are coated in oil. Place the the coins on a baking sheet in a single layer.
Bake the zucchini in the preheated oven for around 1 hour, flipping halfway through.
Heat a skillet over medium heat. Butter the outside of the bread. Arrange the cheese and the zucchini on the buttered bread.
Place the sandwich butter side down on the skillet. Grill for 2-3 minutes or until golden brown. Flip, and grill on the other side until golden brown and the cheese is melted. (I like to put a large saucepan lid on the sandwich to help the process.) Serve immediately.