Bring a pot of salted water to a boil. Add the green beans and cook for 2 minutes or until just tender. Place the green beans in a bowl of ice water to cool, then drain and pat dry.
In a large pot with 5 cups of water, place the dried red beans and 1 bay leaf. Bring the water up to a boil for a few minutes, then bring down to a simmer and cook for about 30 to 40 minutes or until soft. Drain and set aside. Separately, repeat the same procedure to cook the white beans.
Shuck and clean the corn. (Don’t worry about removing every piece of silk, as it will burn on the grill.) Heat your grill to medium hot. Place the corn directly on the grill. Grill turning occasionally for about 10 minutes or until charred and cooked through. (Alternatively, you could just heat up a heavy cast iron pan on high heat and cook the kernels at once with a tablespoon of olive oil just to give them a char, and cover them to steam for about two minutes.)
Place the cooked red beans, white beans, green beans, charred corn, red onion and parsley in a large bowl.
In a small bowl, whisk together the ingredients for the vinaigrette.
Pour the dressing over the beans and toss to coat. Cover the bowl and refrigerate the salad for at least 2 hours or up to three days, then serve.