For the short ribs: Preheat the oven to 300 degrees F.
Trim excess fat and sliverskin from the short ribs and then slice between the bones. Heat the canola oil in a large skillet and sear the short ribs, working in batches.
Transfer the ribs to a hotel pan or roasting pan. Add the cola, soy sauce, rice wine, garlic, green onions, ginger and 2 cups water. Cover with foil and transfer to the oven. Braise for 4 hours, until tender. Shred the short ribs.
For the onion jam: Heat the olive oil in a large skillet. Add the red onions and saute until caramelized, about 10 minutes. Add the brown sugar and honey, and deglaze with the red wine. Stir in the salt, pepper and balsamic. Cook until reduced to a jam consistency. Chop in a food processor.
For the grilled cheese: Preheat a griddle over medium heat. Toast the sourdough slices and then spread them with the butter. Place five of the buttered slices on the griddle; divide the American, cheddar and Swiss cheeses evenly among them. Top each with 5 heaping tablespoons of the shredded short ribs and 1 tablespoon of the onion jam. Cover with a second slice of the toasted bread and cook until the cheeses have melted. Slice in half and serve with marinara sauce, for dipping.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.