Preheat the oven to 400 degrees and line rimmed baking sheet or baking dish with parchment paper.
Cut the zucchinis down the middle, length-wise, and scoop out the seeds and flesh (save for another purpose), leaving about 1/2 an inch of the zucchini shell. Lay the zucchini halves, cut sides up, in the baking pan and sprinkle generously with salt and pepper.
Remove the seeds and chop the tomatoes small. Add the oregano, vinegar, and more salt and pepper to taste to the tomatoes and then divide the tomatoes evenly among the zucchini.
Bake the tomato stuffed zucchini until the zucchini is tender, about 20 minutes. Remove from the oven.
Slice the mozzarella thin and then tear it into 1 inch pieces. Place on top of the tomatoes.
Broil the mozzarella until it starts to bubble and brown just a bit, taking care no to burn it. Remove from the oven and serve hot.