1. Bring a pot of salted water to a boil. Add whole zucchini and cook until a fork inserted in thickest parts meets little resistance, about 8 minutes; drain. When cool enough to handle, cut into 1-inch rounds.

2. Heat oil with garlic and chile in a large skillet over medium, stirring occasionally. When garlic is pale golden (about 3 minutes), remove from heat and carefully add wine (it will splatter). Return to medium and cook at a gentle simmer until liquid is reduced to 2/3 cup, about 11 minutes. Stir in vinegar and 2 teaspoons salt; bring to a boil and add zucchini, tossing to coat. Simmer over medium-high, stirring occasionally, until zucchini is soft and has absorbed some of sauce, about 3 minutes.

3. Remove from heat; stir in mint. Transfer to a serving bowl and let stand 30 minutes, tossing occasionally. Serve at room temperature.