Rinse the beef bones thoroughly under cold water. Soak them in a large pot filled with cold water for at least 30 minutes, or up to several hours, to draw out impurities. Change the water a few times during the soaking process.
Drain the bones and place them in a large stockpot. Add the beef brisket, garlic, and ginger. Pour in 12 cups of fresh water.
Bring the pot to a boil over high heat. Once boiling, reduce the heat to low, cover, and simmer for at least 4 hours, or up to 8 hours, skimming off any scum that rises to the surface periodically. The longer it simmers, the richer and more flavorful the broth will be.
After simmering, remove the beef brisket from the pot and set aside to cool slightly. Strain the broth through a fine-mesh sieve lined with cheesecloth into a clean container. Discard the bones, garlic, and ginger.
Once the brisket is cool enough to handle, slice it thinly against the grain.
Return the strained broth to the pot and bring to a simmer. Season with salt and pepper to taste.
To serve, place a portion of cooked rice in a bowl. Ladle the hot broth over the rice. Top with slices of beef brisket, scallions, salted shrimp (if using), and kimchi (if using). Serve immediately and enjoy!
Notes
Adjust the simmering time based on the desired richness of the broth. For a richer broth, simmer for a longer period.