Put the white beans in a pot with cold water and bring up to a boil. Boil for 2 minutes, then remove from the heat and let rest for 1 hour. Pour off water and add 6 more cups cold water. Bring up to a boil and simmer the beans until tender but not soft. Add 1 teaspoon salt halfway through cooking time. Drain the beans and transfer to a mixing bowl. While warm, dress with 1/3 cup of the olive oil, 1/4 cup of the vinegar, and salt and pepper.
Warm the remaining 2/3 cup olive oil in a saute pan and heat the garlic and sun-dried tomatoes for just a minute or two. Add half this mixture to the beans and mix well.
When the beans are cool, add the chopped onions. Season with salt and vinegar to taste. Combine the rest of the sun-dried tomato oil with the remaining 4 tablespoons of vinegar.
To cook the shrimp, saute in the reserved sun-dried tomato vinaigrette or broil and then toss with the vinaigrette before placing atop bean salad.
Just before serving fold in 1/4 cup chopped basil and top with the cooked shrimp that have been tossed in the sun-dried tomato vinaigrette.