In a resealable plastic bag, combine the onion, garlic, ginger, soy sauce, sugar, vinegar and sesame oil. Add the rib eye and toss to coat. Seal the bag and refrigerate overnight.
Drain the meat, pick off the solids and pat dry. In a large skillet, heat the vegetable oil until smoking. Add the meat and cook over high heat, turning once, until lightly browned, 4 minutes. Transfer the meat to a plate and keep warm. Rinse out the skillet and wipe dry.
In a medium bowl, combine the sugar, vinegar, chile paste and soy sauce. Add the kimchi and toss to coat. Heat the skillet until very hot. Add the kimchi and cook over high heat until the liquid is thickened and glossy and the kimchi is browned in spots, about 5 minutes.
In a small bowl, whisk the mayonnaise with the 3 tablespoons of Sriracha.
Scatter the french fries on a platter and top with the bulgogi and kimchi. Drizzle with some of the Sriracha mayonnaise and sprinkle with cheddar, onion, sesame seeds and cilantro. Serve with additional Sriracha.