This is almost too easy. Cut the zucchini in half lengthwise and then carve out a gouge from the center of each half. Put some olive oil on a baking pan and roll the zucchini and the pieces you carved from it in the oil to coat it all. Use your finger to get some in the carved-out area. Then put Mozzarella in the carved-out area. Italian style Mozzarella is nice, but even American sliced Mozzarella works great (as in the photo).
Put the zucchini in the oven at 325°F and bake for about 25 to 30 minutes depending on the size of the zucchini. If the cheese is cooked and the time isn’t up, turn the oven off and let the zucchini sit there a while longer. You want the zucchini to be soft. You will see there is a bit of liquid in the pan and everything will be browned when all is done.
Serve with salt and pepper to taste.