Directions

1. Peel and mince 1 onion, and set aside.
2. In a large, heavy pot, heat olive oil over medium heat. Add chicken breasts; brown on each side for 10 minutes. Add garlic; saute 1 minute. Stir in 1 teaspoon salt, 1 teaspoon pepper, reserved minced onion, and paprika. Saute until onion becomes soft, 3 to 4 minutes. Add 3 cups water; bring to a boil. Reduce heat; cover, and simmer for 30 minutes.
3. Add parsley and scallions; simmer until softened, about 5 minutes more. Transfer chicken to a large bowl to cool. Strain cooking liquid; pour over chicken. Working over the bowl, remove meat from bones; discard skin and bones. Using your fingers, shred meat. Cover, and chill 30 minutes.
4. Cut beans into 1/4-inch-long pieces. Place in a bowl; set aside. Wash, peel, and grate carrots. Place in another bowl; set aside. Bring a large pot of salted water to a boil. Blanch cut beans until just tender, about 2 minutes. Remove beans from water using a slotted spoon. Place in bowl of ice water to cool. Remove from water, and set aside. Return salted water to a boil. Blanch carrots, until just wilted, about 1 minute. Remove with a slotted spoon, and place in a bowl of ice water to chill. Drain carrots, and set aside. Slice remaining onion into thin rounds. Place in a third bowl; cover, and set aside.
5. Wash and peel potatoes. Place in a large bowl; cover with cold water. Set aside.
6. Cover bottom of a medium stockpot with 2 inches of vegetable oil. Heat oil until a frying thermometer registers 375 degrees.Grate a potato over a towel, pat dry, and immediately place in hot oil. Fry until golden brown. Using a slotted spoon, remove potato from oil, and transfer to a large paper-towel-covered surface; drain. Repeat with remaining potatoes, adding vegetable oil if necessary.
7. In a large serving bowl, toss all reserved ingredients with mayonnaise. Season with salt and pepper, and serve.