Preheat the oven to 500 degrees F (260 degrees C). Split rolls open; toast them on a baking sheet in oven while preheating until desired color reached.

Whisk mayonnaise, garlic, and Parmesan cheese together in a small bowl. Refrigerate until ready to use.

Heat olive oil in a large skillet over medium-high heat. Add steak and onion; season with Worcestershire sauce, liquid smoke, and sea salt. Cook and stir until steak browned and onion tender, about 10 minutes.

Spread garlic-Parmesan mayonnaise generously on both halves toasted rolls. Divide steak and onion mixture among bottom rolls, piling high. Top each with 2 slices provolone cheese; sprinkle with Italian seasoning. Place tops on sandwiches; transfer to a baking sheet.

Bake in the preheated oven until cheese melted, about 5 minutes.