Adjust oven rack to middle position and heat oven to 200 degrees F. Heat oil in large Dutch oven over medium-high heat to 350 degrees F. Set wire rack in rimmed baking sheet.
While the oil heats, combine flour, salt, cream of tartar, pepper and salt in large bowl. Toss onions with apple juice and cider vinegar to coat in another bowl. Drain onions and transfer to flour mixture, tossing to coat.
Fry half of onion rings, stirring occasionally and adjusting burner as necessary to maintain oil temperature between 325-350 degrees F., until golden brown and crisp (3-4 min) Drain onions on prepared wire rack and place in oven.
Bring oil back to 350 degrees and repeat with remaining onions. Season with salt and pepper to taste and serve.
Shoestring onions have thinner, crisp coating that highlights the sweet bite of the onions. At their best, shoestrings arrive at the table a salty, crunchy tangle of feathery fried onions that are hard to stop eating.
This thin crisp coating doesn't obscure the sweet union flavor. Apple juice adds not only more acid (thus adding more crunch)but also it's sweetness balances the vinegar. Cream of tartar is used as an acidic activator to boost crunch even more.