Place steak in a gallon-size plastic resealable food storage bag.
In a medium bowl, combine oil, balsamic and sherry-wine vinegar, apple juice, onion, garlic, and 2 tablespoons paprika rub. Pour over steak in plastic bag. Marinate, refrigerated, at least 6 hours and up to overnight, turning every few hours.
Remove steak from refrigerator and let come to room temperature for 1 hour. Preheat grill or grill pan to high heat.
Remove steak from marinade and season with additional paprika rub. Grill for 2 minutes, then rotate steak 90 degrees to create crosshatch marks. Cook for 2 minutes more. Turn steak and repeat process, cooking until steak has reached desired level of doneness. Steak is best served rare to medium-rare to avoid toughness.
Remove steak from grill and let stand 5 minutes before slicing against the grain for serving.
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