Cook beans in large pot of rapidly boiling salted water until just crisp-tender. Rinse with cold water. Drain. Transfer to bowl. Combine shallots and vinegar. Gradually mix in oil. Add basil. Add enough dressing to beans to coat. Gently mix in 2/3 cup cheese. Season with salt and pepper. (Can be made 4 hours ahead. Cover; chill.) Place beans on platter. Top with cheese.