Make an ice-water bath.
Bring a large pot of salted water to a boil. Add both kinds of beans, reduce the heat to medium, and cook for 3 to 4 minutes, until the beans are just tender. Drain and place in the bowl of ice water for a few minutes.
When the beans are cool, drain immediately and place them in a large bowl. Add the garlic, tomatoes, and vinaigrette and toss until mixed. Season with the salt and pepper.
Preheat the oven to 400 degrees F.
Cut off the top 1/3 of the garlic heads crosswise to expose the cloves. Drizzle each head with 1 tablespoon of the oil and wrap in aluminum foil. Place the garlic on a baking sheet and roast in the oven for about 40 minutes, or until soft. Allow to cool, then squeeze garlic cloves out of their skins.
Store the garlic in plastic wrap or covered with olive oil in a glass jar. The roasted garlic will keep for about 2 weeks in the refrigerator.
Place the sun-dried tomatoes in a small bowl. Pour the boiling water over the dried tomatoes to soften, 10 to 15 minutes. Remove the tomatoes, reserving the tomato water.
In a blender or food processor, combine the tomatoes, basil, garlic, vinegar, and 6 tablespoons of the tomato water or plain water and pulse until smooth. With the motor on low, slowly add the oil and blend until the dressing is well blended. Season with the salt and pepper.
If you use tomatoes that are packed in oil, skip the first step of re-hydrating.
Recipe courtesy of Debra Ponzek and Geralyn Delaney Graham, The Summer House Cookbook, Potter, 2003