Cooking the Green Beans:

1. Bring a large saucepan two-thirds full of water to a boil over high heat. Add the 1 tablespoon of salt and the green beans, and cook until the beans are bright green and tender, about 4 to 5 minutes. Drain and immerse the beans in a bowl of ice water to cool. Then drain and set aside.

2. In a small saucepan over medium heat, combine the 1 1/2 cups of white cider vinegar, onion, sugar and salt, to taste. Bring to a boil, separating the onion slices into rings and cook until slightly tender, 1 to 2 minutes. Remove from the heat and allow to cool.

3. In a small bowl, stir together the shallot, mustard, mint and white wine vinegar. Gradually whisk in 4 tablespoons of the olive oil. Season with salt and pepper and set the vinaigrette aside.

4. In a large sauté pan over medium heat, warm the remaining 1 tablespoon of olive oil and add the beans. Sauté, stirring occasionally, until they are warmed through, about 2 to 3 minutes. Drain the onions, discarding the vinegar. Add the onions to the beans. Cook until warmed through, another 2 to 3 minutes more. Add the vinaigrette and toss well to coat. Transfer to a warm serving dish.