16 slices white American cheese (or Monterey jack)
Instructions
Sprinkle the short ribs with salt and pepper. Melt the butter in a large wide pot over medium-high heat. Working in 2 batches, cook the short ribs until browned on both sides, about 3 minutes per side in each batch. Remove the short ribs and transfer to a plate. Add the celery, carrots, and onion to the pot and sauté until beginning to soften and brown while stirring often (about 5 minutes). Add the wine, broth, Sherry, garlic, bay leaves, and thyme sprig. Bring to a boil, scraping up any brown bits off of the bottom of the pan. Season with salt and pepper. Return the ribs to the pot, propping up on the sides and arranging in the single layer. Cover, reduce heat to medium-low and simmer for 1 hour.
Turn the ribs over in the pot. Cover and simmer until the ribs are tender and the sauce is very thick, about 1 ½ hour longer. Uncover and cook for 30 minutes. Transfer the ribs to a work surface. Discard the bay leaves and thyme sprig. Remove the meat from the bones of the short ribs. Discard the bones. Cut the meat into ¾ to 1-inch pieces, trimming any fat. Return the meat to the pot.
Spread butter onto one side of each slice of bread. Top each bread slice with 1 slice of American cheese and some of the chopped short ribs. Top the short ribs with another slice of American cheese. Top with the remaining bread slice.
Heat a large skillet to medium-low heat. Place sandwiches into the skillet butter side down. Spread butter on the top of each sandwich. Cook over medium-low heat for about 6-8 minutes or until the bottom is golden brown. Turn the sandwiches and cook for 5-6 minutes longer or golden brown and the cheese has melted.