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