Wash zucchini, trim both ends, and slice in half lengthwise. Using melon baller, scoop out flesh, leaving 1/8” thick walls. Reserve trimmings.
Brush edges of zucchini halves with a bit of the melted butter and bake, cut side down, in a 350°F oven for 10 minutes.
While zucchini is baking, chop trimmings roughly and place in a medium bowl. Add the cheese, remaining melted butter, salt, pepper and oregano.
Fill zucchini halves with this mixture, tamping down so they don’t overflow.
Increase oven temperature to 375°F. Bake zucchini for 10-15 minutes, or until cheese is melted and is starting to brown. Serve hot.