1.Boil, steam or microwave asparagus and snow peas, separately, until just tender; drain. Rinse under cold water; drain.
2.To make basil dressing, place ingredients in screw-top jar; shake well.
3.Arrange lettuce on platter; top with asparagus, snow peas and beans, drizzle with a quarter of the dressing. Arrange tomato, cheese and basil on top; drizzle with remaining dressing.
Many varieties of already cooked white beans are available canned, among them cannellini, butter and haricot beans; any of these is suitable for this salad.