Make Spiced Mayonnaise: Whisk the Marinade ingredients together in a Ziploc bag. Remove 1 tablespoon and mix it with ½ cup mayonnaise in a small bowl to make "Spiced Mayonnaise." Store in the refrigerator.
Marinate Steak: Add the thinly sliced steak to a Ziploc bag with the remaining marinade. Marinate for 6 hours or overnight. Remove the steak from the fridge 20-30 minutes before cooking.
Preheat the oven to 400°F.
Slice each hoagie roll in half horizontally. Hollow out the bottom and top halves of the bread, leaving about a ½-inch shell.
Cook Meat: Heat 1 teaspoon of olive oil in a large cast iron skillet over medium-high heat until smoking. Pat excess marinade off of the steak and add it to the skillet. Cook without stirring for 1 minute, then continue cooking while stirring just until the meat is no longer pink, about 1-2 minutes, chopping it up with a spatula as you cook. Remove to a paper towel-lined plate. (You can also chop on a cutting board or chop finer on a cutting board-the key is not to overcook.) Drain off any liquid that accumulates as the steak cooks.
Sauté Veggies: Wipe out the skillet and heat one tablespoon of olive oil over medium-high heat. Add the peppers and onions and cook 6-8 minutes or until softened.
Add the steak back to the pan along with ¾ cup cheddar. Stir just until the steak is warmed through and cheese begins to melt, about 1 minute—season with salt and pepper to taste.
Assemble: Spread the hoagie roll with the Spiced Mayonnaise. Evenly divide the beef mixture between the bottom buns, then top each with 2 slices of provolone cheese.
Bake hoagies open faced for 5 minutes or until the cheese is completely melted. Replace top buns and eat immediately.
