Bring a large pot of water to a boil. Add beans and cook until bright green, 2 to 3 minutes. Transfer to a colander using a slotted spoon; refresh under cold water.dd potatoes to the boiling water. Cook until tender when pierced with a fork, 8 to 10 minutes. Drain in a colander; refresh under cold water until room temperature.
Toss the green beans and potatoes with crab, celery, radishes and onion in a large bowl.
Whisk garlic, lemon juice, vinegar and mustard in a small bowl; slowly whisk in oil. Whisk in basil, salt and pepper. Discard the garlic; pour the dressing over the salad and toss to coat.