1. Heat a large Dutch oven or heavy-bottomed pot over medium-high heat and coat the bottom with a drizzle of oil.
2. Generously season bone-in beef short ribs with salt and pepper, then sear them in batches, browning all sides evenly for about 3-4 minutes per side. Remove and set aside.
3. Reduce the heat to medium and melt unsalted butter in the pot.
4. Add thinly sliced yellow onions and cook, stirring frequently, for 12-15 minutes until caramelized to a golden-brown hue. Cover the pot for the first 5 minutes to help the onions sweat.
5. Stir in minced garlic, chopped carrots, tomato paste, and fresh thyme sprigs, cooking for 2-3 minutes until fragrant.
6. Pour in red wine or dry sherry, scraping the bottom of the pot to deglaze and release browned bits. Allow the liquid to reduce by half, taking 3-5 minutes.
7. Return the seared short ribs to the pot and pour in beef broth. Add a bay leaf and bring the mixture to a simmer.
8. Cover the pot with a tight-fitting lid and simmer over low heat for 2.5-3 hours, or transfer to a slow cooker on low for 7-8 hours.
9. Once cooked, remove the short ribs, shred them into bite-sized pieces, and discard the bones and excess fat. Strain the broth to remove thyme sprigs and the bay leaf.
10. Return the shredded short ribs to the strained broth and stir in the caramelized onions. Adjust salt and pepper to taste.
11. Preheat your oven to 350°F and slice a French baguette into 1-inch thick pieces.
12. Arrange the slices on a baking sheet and lightly toast them for 5-7 minutes until semi-crisp.
13. Rub one side of each toast slice with a cut garlic clove and top with shredded Gruyère cheese.
14. Return the toasts to the oven and broil for 1-2 minutes until the cheese melts and turns bubbly and golden.
15. Ladle the steaming hot soup into serving bowls and top each portion with the cheesy Gruyère toast. Optionally, float the toast on the soup.
16. Garnish with chopped chives or parsley for a fresh finish.
17. Serve immediately and enjoy your comforting French Onion Short Rib Soup with Cheesy Gruyère Toast.