Cutting against the grain, slice the steak into thin strips, then cut those slices into ½" pieces.
In a large skillet, melt butter. Add minced garlic and heat until fragrant. Then add sliced steak and cook until browned. Transfer the cooked steak and discard any liquid from the pan.
Add peppers, mushrooms, and onions to the same skillet and cook until vegetables are tender and the liquid has evaporated.
To a mixing bowl, add egg, shredded mozzarella, cream cheese, pepper, and salt.
Using an electric mixer, mix until well combined.
Stir in the cooked steak and vegetables.
Transfer the mixture to the baking dish and arrange the provolone cheese slices evenly on top of the mixture. Bake until the edges of the casserole are golden brown and bubbling.
Remove the baking dish from the oven and allow the casserole to cool before slicing and serving.