Thoroughly rinse the beef marrow bones under cold running water. Submerge the bones in a large bowl filled with cold water and soak for at least 1 hour to extract excess blood. For optimal results, extend the soaking time as desired, changing the water occasionally.

Repeat the soaking process in a separate bowl for the beef brisket or shank meat. Once completed, drain the meat and refrigerate until needed.

Place the soaked bones into a large stockpot (preferably 8 quarts or larger). Fill the pot with enough cold water to completely submerge the bones. Bring to a vigorous boil over high heat, then reduce to medium heat and continue boiling for 5 minutes. Drain the water, discard impurities, and rinse the bones thoroughly. Clean the stockpot to remove any remaining residue.

Return the cleaned bones to the pot. Add fresh cold water, leaving adequate space at the top to prevent boiling over. Bring the pot to a boil over high heat, then lower the heat to maintain a steady medium boil. Cover the pot and simmer for approximately 5 hours, or until the broth achieves a rich, milky consistency. Add additional hot water as necessary to keep the bones submerged during this process.

Once the broth appears sufficiently milky, add the soaked brisket or shank meat to the pot. Ensure the meat is fully submerged. Continue to boil for an additional 1.5 to 2 hours, or until the meat becomes tender. Remove the meat from the broth and allow it to cool. Thinly slice the meat and reserve for serving.

Strain the initial broth through a fine colander into a separate pot or large bowl. Refill the stockpot with fresh water and return the bones. Bring to a boil and then simmer, covered, for an additional 3 to 5 hours, maintaining a steady medium boil. Strain and combine with the first batch of broth for a deeper flavor. This process may be repeated once more if desired.

Allow the broth to cool slightly. Use a fat separator to remove excess fat. Alternatively, refrigerate the broth until the fat solidifies on top, then skim off the hardened fat.

To serve, place a portion of cooked rice or noodles into individual bowls. Arrange thin slices of cooked brisket on top. Ladle the hot broth over the contents of each bowl. Provide additional garnishes of chopped scallions, along with small dishes of salt and pepper, allowing diners to season the soup according to their preferences. Serve immediately with kimchi or other side dishes.