Add mesquite seasoning ingredients to small mixing bowl and stir with spoon. Set 1⁄4 of mixture aside for spicy mayo aioli.
Brush flank steak evenly with olive oil. Coat with mesquite seasoning.
Place flank steak in resealable freezer-safe bag. Pour bottle of your favorite beer into bag and seal, removing as much air as possible. Refrigerate marinated steak for at least 3 hours; overnight is best.
Remove flank steak from resealable bag and sear on piping-hot griddle until internal temperature reaches 145°F as measured with meat thermometer for medium doneness, turning only once halfway through grilling time.
Remove from grill and let stand for 3 minutes before slicing against grain into ¼-inch strips.
Mix remaining mesquite seasoning with mayo to prepare spicy mayo aioli. Spread onto toasted buns.
Layer thinly sliced flank steak onto bun and top with slice of provolone cheese.
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