In a bowl, combine the thinly sliced steak with the Italian dressing, Worcestershire sauce, minced garlic, salt, pepper, and red pepper flakes. Mix well and let it marinate for at least 30 minutes.
Preheat your oven to 475°F (245°C) if you're using a pizza stone or 450°F (232°C) for a baking sheet.
In a large skillet, heat a tablespoon of oil over medium heat. Add the sliced mushrooms, red onion, and green pepper. Sauté until they are tender and slightly caramelized, about 6-8 minutes. Remove from heat and set aside.
In the same skillet, add the marinated steak. Cook over medium-high heat until browned and cooked to your desired doneness, about 3-4 minutes for medium rare. Remove from heat.
Roll out your pizza crust on a floured surface to your desired thickness. If using a pizza stone, transfer the rolled-out dough onto a floured pizza paddle or baking sheet. Spread the Alfredo sauce evenly over the crust. Layer the sautéed vegetables and cooked steak on top, followed by the shredded mozzarella cheese.
Carefully transfer the pizza to the preheated oven. Bake for 12-15 minutes, or until the cheese is bubbly and the crust is golden brown.
Once baked, remove the pizza from the oven and let it cool for a few minutes. Slice it up and enjoy your homemade Philly Cheese Steak Pizza with your favorite dipping sauce if desired!