Preheat oven to 475 degrees. On two large rimmed baking sheets, toss zucchini with 2 tablespoons extra-virgin olive oil; season with coarse salt and ground pepper. Roast until zucchini are tender and undersides are browned, 10 to 15 minutes.
On a serving plate, sprinkle zucchini with minced garlic and drizzle with 2 tablespoons oil and white-wine vinegar. Let stand 1 hour (or refrigerate, up to overnight; bring to room temperature before serving). To serve, sprinkle with torn mint leaves.