1. Preheat charcoal or gas grill to medium heat.
2. Rub 1 tablespoon olive oil evenly over onions. Sprinkle evenly with 1/4 teaspoon salt and 1/4 teaspoon pepper. Grill 6 minutes or until well marked and greens are tender, turning occasionally. Cool completely.
3. Combine Dijon mustard and vinegar in a small bowl, stirring with a whisk. Gradually add remaining 2 tablespoons olive oil, stirring with a whisk. Stir in parsley, tarragon, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper.
4. Arrange 2 onions on each of 4 plates, and top evenly with tomatoes. Drizzle 1 tablespoon vinaigrette over each salad; top evenly with sliced eggs and minced chives.