1. Adjust oven rack to middle position and heat oven to 200 degrees. Heat oil in Dutch oven over medium-high heat until 350 degrees.
2. Meanwhile, combine flour, 1 teaspoon salt, cream of tartar, and ½ teaspoon pepper in large bowl. Toss onions, apple juice, and vinegar to coat in another bowl. Drain onions and transfer to flour mixture, tossing to coat.
3. Fry half of onion rings, stirring occasionally and adjusting burner as necessary to maintain oil temperature between 325 and 350 degrees, until golden brown and crisp, 3 to 4 minutes. Drain onions on wire rack set in rimmed baking sheet and place in oven. Bring oil back to 350 degrees and repeat with remaining onions. Season with salt and pepper to taste. Serve.
**Apple juice and apple cider vinegar are both flavorful and acidic. Their acid is key here, because it draws more amylose out of the starch granules as they gelatinize (or absorb water). The amylose makes the coating crisp when the gelatinized starch is fried in oil.