Mix shallot and two tablespoons of vinegar in a small bowl. Allow to marinate for at least 30 minutes.
Steam or parboil green beans until crisp-tender, from 3-5 minutes, depending on their size. Rinse under cold water. Drain well.
Drain shallots and return to small bowl.
Combine chopped basil and mint. Set aside two tablespoons; mix the remaining herbs into the shallots.
Place a slice of tomato on outer edge of plate; partially cover with a slice of chèvre. Sprinkle the cheese with about a teaspoon of the onion mixture. Repeat with the remaining tomato slices, cheese, and onion mixture.
Place green beans in center of plate.
Sprinkle tomatoes and cheese with reserved herb mixture. Season salad with salt and pepper.
Just before serving, drizzle salad with olive oil and additional red wine vinegar to taste.