Mix the soy sauce, brown sugar, sesame oil, garlic, and ginger in a bowl. Add the sliced ribeye, toss to coat, and let marinate for 20 minutes. Drain excess liquid before cooking.
Heat the vegetable oil in a large cast-iron skillet over medium-high heat. Cook the sliced onions for 2 minutes until soft.
Add the marinated beef to the skillet in a single layer. Let sear for 1 minute undisturbed, then toss with the onions and cook for 2 more minutes. Stir in the chopped kimchi.
Divide the meat mixture into four portions in the pan. Top each with two slices of provolone. Cover the skillet for 60 seconds to melt the cheese.
Scoop each cheesy portion using a large spatula directly into the toasted hoagie rolls and serve immediately.
