Make Light Aioli: Place garlic, egg yolks, vineger, 2 T. lemon juice, the salt, and cayenne in food processor or blender and process until garlic is pureed. With machine running, add both oils in thin, steady stream to make mayonnaise.
Transfer mayonnaise to serving bowl and fold in 3 T. yougurt. Taste and add more yogurt and lemon juice if needed. Mayonnaise should have a pleasant tang. Refrigerate covered at least 30 minutes to allow flavors to blend.
Place beef broth, the water, onion, and bay leaf in Dutch oven or heavy casserole large enough to fit beef without crowding; heat to boiling. Place beef in boiling broth and add water if needed to completely immerse meat. Adjust heat to maintain a steady simmer, cover pan, and cook until instant-read thermonmeter inserted in center of beef reads 125 degrees, about 25 minutes. Transfer beef to platter and let stand to cool.
Meanwhile, add leeks and carrots to broth; simmer covered about 15 minutes. Add green beans and continue to simmer just until vegetables are tender, about 5 minutes. Transfer vegetables to a second platter to cool completely. Reserve broth for other use.
Using vegetable peeler, remove strip of peel from the middle of each potato. Place potatoes in saucepan and add cold water to cover. Heat to boiling. Salt water and boil potatoes covered just until tender, 10-20 minutes. Drain, rinse under cold running water, and transfer to platter of vegetables to cool.
Beef and vegetables should be served cool at room temperature. If necessary, refrigerate lightly covered.
To serve, cut beef into 1/4"-thick slices. Arrange beef slices overlapping on large platter, then arrange vegetables around beef. Garnish with watercess. Pass aioli.