01 - Preheat oven to 325°F. Heat olive oil in a Dutch oven over medium-high heat. Season short ribs with salt and pepper. Sear all sides until deep brown, 4 minutes per side. Remove and reserve.
02 - Add diced onion and minced garlic to the Dutch oven. Cook until tender and fragrant, approximately 3 minutes.
03 - Stir in tomato paste, then deglaze with red wine, scraping up browned bits. Pour in beef broth, add thyme and bay leaf.
04 - Return short ribs to the pot, cover, and transfer to oven. Braise for 2.5 to 3 hours, until meat is fork-tender.
05 - Remove short ribs and discard bay leaf. Shred beef with two forks. Skim fat from sauce, add 2 to 3 tablespoons to the shredded meat for added flavor.
06 - Butter one side of each bread slice. Arrange 4 slices, butter-side down, on a work surface. Top evenly with cheddar, Gruyère, and short rib. Crown each with a second bread slice, butter-side up. Optionally, substitute mayonnaise for butter on exterior for extra crisp texture.
07 - Heat a large skillet or griddle over medium heat. Cook sandwiches 3 to 4 minutes per side, pressing gently, until bread is golden brown and cheese is melted.
08 - Slice sandwiches and serve immediately while hot.