Preheat the oven to 350°F (177°C). Place the marrow bones on a baking sheet (sheet pan) and roast for 20-40 minutes, depending on the size and cut of bones, until the marrow is soft and slightly browned.
While the bones are roasting, peel and dice the carrots, dice the celery, and peel and dice the onion. This is your mirepoix. Set aside.
Remove the marrow bones from the oven and place the baking sheet on a heatproof surface. Allow the bones to cool slightly. Once you can handle the bones comfortably, do the following for each bone: scoop out the bone marrow, place it into a bowl, and set aside. Place the cleaned-out bones in a second bowl and set aside.
Place a medium saucepan or soup pot on the stovetop and add the ghee. Melt the ghee over medium heat, then add the onion, carrot, and celery. Sprinkle with sea salt and black pepper. Sauté the mirepoix for 5-7 minutes until soft and fragrant.
Sprinkle the flour over the mirepoix and cook for an additional 1-2 minutes to build the base. Stir continuously to remove the raw flour taste.
Pour the white vermouth into the soup pot and stir well to deglaze the soup pot. Scrap up any brown bits that have formed on the bottom of the pan.
Add the roasted bones to the soup pot and stir.
Pour the beef broth into the soup pot and add the bay leaf. Bring the mixture to a boil, then immediately reduce to a low simmer. Cover the soup pot and let the mixture simmer gently for 1 hour to extract the nutrients from the bones. After 1 hour, remove the bones from the broth.
Add the bone marrow to the soup pot and use a stick blender to purée the soup and incorporate the bone marrow. Blend until smooth. (Alternatively, you can purée the soup with the bone marrow in a blender. Blend until smooth.)
Allow the soup to simmer uncovered for an additional 2 minutes to meld the flavors.
Remove the bay leaf, then ladle the soup into bowls and garnish it with freshly chopped herbs, such as parsley, chives, or thyme, for a pop of color and added flavor. Serve and enjoy this luxurious and deeply satisfying soup!