Preheat oven to 400°.
Cut onions in half vertically. Drizzle the cut side of each onion half with 1/4 teaspoon oil. Sprinkle halves evenly with salt and pepper. Place 1 thyme sprig on 1 onion half; top with other half. Wrap in foil. Repeat procedure with the remaining thyme and onion halves. Bake the wrapped onions at 400° for 1 hour or until tender. Cool to room temperature. Discard thyme, and chop onions. Combine 1 tablespoon olive oil, onion, dill, vinegar, and mustard in a small bowl.
Toss the beans with the vinaigrette.