Heat a large pot over medium-high heat. Add the beef short ribs and sear until browned on all sides, about 5-7 minutes. Remove and set aside.

In the same pot, add the sliced yellow onions. Cook over medium heat, stirring occasionally, until golden-brown, about 20-25 minutes.

Return the seared short ribs to the pot and pour in the beef broth. Add thyme leaves and balsamic vinegar. Bring to a boil, then reduce heat and simmer for an hour.

After simmering, remove the short ribs and shred the meat into bite-sized pieces, discarding bones. Return the shredded beef to the pot.

Ladle the soup into bowls and sprinkle shredded Gruyère cheese on top. For a gooey finish, broil for about 5 minutes until golden.