Add oil to a heavy-bottomed pot over medium-high heat. Once the oil is hot, add the beef shank, searing until a crust forms. Flip the meat over and sear the other side. Remove the beef from the pot.
Add the two halves of the garlic bulb to the pot, cut side down. Stir, cooking until the garlic until charred and golden brown. Add the star anise and black pepper. Quickly toast the spices until fragrant.
Add the water, ½ cup soy sauce, and beef into the pot. Once the liquid starts boiling, reduce the heat to low. Cover and cook until the beef is fork-tender, about 3 hours.
Remove the beef from the pot and transfer to a cutting board. (Reserve about 1 ½ to 2 cups of braising liquid.) Chop the beef with a knife or shred it with a fork until you get small, half-inch pieces.
Combine ¼ cup soy sauce, brown sugar, and ½ cup braising liquid in a pan over medium-high heat. Once the liquid is simmering, add the chopped beef. Cook until the liquid has reduced to a glossy sauce, coating the meat. Serve with garlic rice, sunny-side-up, and atchara.
