Marinate the beef: Whisk the soy sauce, sesame oil, brown sugar, gochujang, and garlic in a bowl. Add the sliced ribeye and toss to coat. Let sit for 15 minutes.
Cook the onions: Heat a skillet over medium-high heat with the oil. Add sliced onions and cook for 3 minutes until softened.
Sear the meat: Push the onions to the side. Add the marinated beef to the center of the pan. Let it sear for 1 minute before stirring.
Add the kimchi: Fold in the chopped kimchi. Cook everything together for 3 more minutes until the beef is fully cooked and the pan juices reduce into a glaze.
Melt the cheese: Divide the meat into 4 portions in the pan. Top each with a slice of provolone cheese. Turn off the heat and cover the pan for 60 seconds to melt the cheese.
Assemble: Toast the hoagie rolls in a separate pan. Use a spatula to transfer the cheesy meat portions directly onto the toasted rolls and serve warm.