Heat 1 tablespoon oil in a deep, 12-inch nonstick skillet over MEDIUM heat until shimmering. Add the ground beef and ½ teaspoon salt and cook, breaking up the beef with a spoon, until crumbled and browned. Drain off as much of the excess grease as possible and transfer the cooked beef to a plate and set aside.
Return the skillet to the heat and add the remaining oil, the onion and ¼ teaspoon of the salt, and sauté, stirring frequently, until softened and beginning to brown, about 5 minutes. Stir in the bell pepper, mushrooms, and garlic, and cook, stirring frequently, for 3 to 4 minutes until bell peppers and mushrooms begin to soften and garlic is fragrant. Add the cooked ground beef back to the skillet along with the remaining ¼ teaspoon salt, Italian seasoning, and garlic pepper. Cook, stirring, for a minute or two.
Stir the uncooked pasta into the beef and pepper mixture. Pour in the beef broth and increase the heat under the skillet as needed to bring the mixture to a boil. Reduce heat to LOW, cover, and cook for 15 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed.
Stir the pepper jack cheese into the pasta and place the provolone slices in a circle over the top. Cover and cook until the cheese has melted and serve.