In a medium mixing bowl add the mayonnaise, garlic, lemon juice, and salt and stir. Set aside.
To a large bowl add the steak, brown sugar, balsamic vinegar, vegetable oil, salt, and pepper, and toss well.
In a cast-iron skillet on medium heat add butter and onions.
Cook, stirring often, for 10-12 minutes until they've caramelized.
Remove the onions.
Raise heat to high and add steak, letting marinade drip off before you add to the pan.
Sear on each side for 3-4 minutes.
Let rest for 5 minutes, then slice against the grain thinly.
Brush hoagies with melted butter and place buttered side down onto a griddle or pan to brown for 2-3 minutes.
Spread with garlic aoili, Provolone cheese, greens, and top with steak and onions.