For the caramelized onions: Melt butter in a medium saute pan over medium heat. Add onions and cook, stirring every few minutes with a metal spoon or spatula, until a rich chocolate brown color, 30 to 45 minutes. (Do not stir too often or onions will not properly caramelize; stir often enough to prevent onions from burning.) Deglaze pan with red wine and cook an additional 2 to 3 minutes.
For the short ribs: Preheat oven to 350 degrees F.
Heat bacon fat in a medium stockpot over medium-high heat. Add the celery, carrots and onions and cook until onions are browned, 5 to 7 minutes. Add tomato paste and stir constantly until well combined and deep red, 3 to 4 minutes. Stir in wine and bring to a boil. Add all herbs and garlic and stir in beef stock. Bring to a boil. Reduce heat and let braising liquid simmer while preparing short ribs.
Trim excess fat from short ribs and cut into four 5- to 6-ounce portions. Sprinkle all sides of the short ribs with salt and pepper. Brush bottom of a large Dutch oven with a little vegetable oil and heat until smoking hot. Add short ribs. Brown all sides and turn off the heat; turn off the heat to the braising liquid as well.
Carefully ladle all the braising liquid along with the herbs and vegetables over the short ribs. Cover cook in the oven, 4 hours.
Using metal tongs, carefully remove each short rib from the braising liquid and set aside to cool. Strain braising liquid. Discard vegetables and herbs, reserving liquid. Set aside.
Raise oven temperature to 375 degrees F. Slice short ribs and remove any excess fat. Heat braising liquid in a medium pot. Add sliced short ribs and caramelized onions and heat approximately 5 minutes. Remove short ribs and caramelized onions and place inside French rolls; arrange on a baking sheet. Top with Gruyere and toast in oven until cheese is well melted, 5 to 7 minutes. Serve with coleslaw and a cup of warm braising liquid for dipping.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.