Cut the zucchini crosswise into 3-inch (8-centimeter) pieces. Cut each piece in half lengthwise, then cut out all the seeds and spongy pulp from the center. Slice each section crosswise 3?16 inch (41/2 millimeters) thick. (A mandoline or other manual vegetable slicer is helpful for this.)
Make layers of sliced zucchini and salt in a large bowl, then toss well. Macerate for 12 hours to draw the water out of the zucchini. Drain the zucchini, then squeeze a handful at a time to remove excess water.
Place the zucchini in a heavy nonreactive pot and add the vinegar and 1 cup (250 milliliters) water. The liquid should barely cover the zucchini.
Bring to a boil over high heat. Stir to redistribute the zucchini, then reduce the heat to medium and cook until the zucchini slices are cooked through but still whole, about 5 minutes. Do not allow them to break apart. Smaller zucchini will take less time.
Drain the zucchini and put them in a large colander. Top them with a heavy weight, such as a pot filled with water, to squeeze out the liquid. Let the zucchini drain under the weight for 15 minutes.
Lay several clean kitchen towels on a table covered with cardboard. Arrange the zucchini slices on the towels, spreading the slices apart. Let dry at room temperature until they feel a little leathery and are no longer damp, 24 to 48 hours. They will shrivel considerably.
Place the zucchini in a bowl and toss with the mint, garlic, hot peppers, and the 1/2 cup (125 milliliters) olive oil. Taste for salt and let the mixture marinate at room temperature for a day.
Transfer the zucchini to a 1-pint (1/2-liter) glass jar. Pack them in tightly, pushing them down with a fork or spoon to remove any air gaps. Top with olive oil so they are completely submerged. Cover and refrigerate for at least 2 weeks before sampling to give the zucchini time to absorb the seasonings.
Bring them out of the refrigerator about an hour before you plan to serve them to allow the oil to liquefy. Return any leftover zucchini to the refrigerator, topping with oil so the zucchini remain completely submerged. If kept submerged in olive oil and refrigerated, the zucchini will last for up to 6 months.