Wash, dry, and trim the zucchini. Cut them crosswise into rounds approximately ¼ inch thick.
Arrange the slices in a colander or on a wire rack and sprinkle them lightly with the coarse sea salt. Let them drain for around 30 minutes.
Brush off the excess salt and blot the zucchini thoroughly with paper towels or a clean kitchen towel.
Heat the frying oil in a deep, heavy-bottomed pan to approximately 350°F or 175°C.
Fry the zucchini in small batches for 2 to 3 minutes, turning as needed, until golden around the edges and tender.
Transfer the fried zucchini to a paper-towel-lined plate or wire rack and repeat with the remaining slices.
Layer the warm zucchini in a shallow serving dish, scattering the garlic and fresh mint between the layers.
Drizzle with the white wine vinegar and 2 teaspoons of fresh extra-virgin olive oil. Gently turn the zucchini to distribute the seasoning.
Taste and add a small amount of salt only if needed.
Cover and refrigerate for at least 2 hours, or preferably overnight.
Remove from the refrigerator 20 to 30 minutes before serving. Serve cool or at room temperature.