Heat oven to 325°F. Generously season the ribs on all sides with salt and pepper.

In a large Dutch oven, heat the oil over medium-high heat. Brown half of short ribs on all sides; set aside and repeat with the second half.

If there’s a lot of fat in the pot, pour it off until you have 2 tablespoons left. Add carrot, onion, leek (if using) and cook until lightly browned, about 5 to 6 minutes. Season with salt and pepper.

Add tomato paste and cook for 2 minutes. Add the red wine and cook until it has reduced to just a puddle, about 3 minutes.

Return the short ribs and any juices to the pot. Add garlic, thyme sprigs, and bay leaf, then pour broth over ribs and vegetables. Cover and braise until the short ribs are falling off the bone, about 2 ½ to 3 hours.

Meanwhile, melt butter over medium heat. Add the onions, toss to coat them in butter and cover. Reduce heat to medium-low and let them steep for 15 minutes.

Uncover the pot, raise the heat slightly and stir in salt. Cook onions, stirring every 5 minutes for about 40 to 90 minutes until caramelized.

When the short ribs are cooked, remove them from the broth and strain the broth, discarding the vegetables.

Place the caramelized onions in the final soup pot and rewarm over medium-high. Add broth and bring to a simmer, season to taste.

Add short ribs to broth and gently simmer together for 10 to 15 minutes.

To make the cheese toasts, heat your oven’s broiler. Toast the bread until semi-firm and dry, rub with garlic, divide cheese between toasts, and broil until melted.

To serve, ladle ribs and broth into bowls and sink a cheese toast halfway in. Sprinkle with chives.