Whisk together soy sauce, brown sugar, garlic, gochujang, and sesame oil in a medium bowl until the sugar dissolves. Add the sliced ribeye and toss to coat evenly. Let marinate at room temperature for 15 minutes, or refrigerate up to 2 hours.

Heat your cast-iron skillet over high heat until smoking. Working in two batches to avoid crowding, add the marinated beef in a single layer. Sear undisturbed for 90 seconds until deeply browned, then flip and cook 30 seconds more. The beef should be caramelized at the edges but still juicy. Transfer to a plate and repeat with remaining beef.

Reduce heat to medium-high. Add the drained kimchi to the hot skillet and cook for 2 minutes, stirring occasionally, until it softens and the edges char slightly. Return all beef to the pan and toss together for 30 seconds to combine.

Split the hoagie rolls and spread the softened butter on the cut sides. Toast cut-side down in a clean skillet or under the broiler until golden, about 2 minutes.

Divide the beef-kimchi mixture among the bottom halves of the rolls. Layer two slices of provolone over each mound of meat. Return to the broiler for 1-2 minutes until the cheese is fully melted and bubbling with light brown spots. Close the sandwiches, sprinkle with sesame seeds, and serve immediately.