Make the vinaigrette but combining all the ingredients except the olive oil in a blender. Puree. Add 1/2 cup oil and puree again. Add more oil as needed to make a thick sauce, but don't over blend it.
Cover the potatoes with water in a saucepan, bring to the boil, add 1 teaspoon salt and reduce heat. Simmer until the potatoes are cooked but not soft, about 15 minutes. Drain, rinse with cold water and let cool.
In a saucepan of boiling water, blanch the beans for two minutes. Drain and rinse with cold water.
Cut the potatoes into 5mm slices and arrange with the green beans and crab meat on a platter. Garnish with cherry tomatoes and drizzle with some of the pesto vinaigrette.