Chop carrot, celery, and yellow onion into medium pieces. Season osso buco with salt and pepper, coat in flour, and brown both sides in a deep skillet with olive oil. Remove and set aside.
In the same skillet, sauté the chopped vegetables.
Add tomato paste, then beef broth. Return osso buco to the skillet, top with thyme, cover, and simmer on low heat for 2 hours.
Once cooked, shred the meat into small pieces, mix with some broth for moisture. Prepare sauce: combine mayonnaise, ketchup, Worcestershire sauce, mustard, salt, and pepper to taste; mix well.
Slice bread lengthwise, spread sauce, layer with red onion rings, shredded meat, and cheese. Top with the second bread slice and bake in a preheated oven at 180°C (350°F) for 3 minutes.
Enjoy your juicy, delicious sandwich!