While the dashi is cooking, pat dry the short ribs as needed then sprinkle all over with salt and pepper. Heat the oil over a medium-high heat in a pot/pan with a lid large enough to hold the ribs in one layer relatively snuggly.
Brown the short ribs all over well so they get a good level of browning. Make sure you give them time to brown before turning and increase heat if needed to get a good sear.
Once browned all over, add the soy, mirin, sugar, ginger and garlic to the pan with the ribs. Turn the meat to coat in the mixture. Add the strained dashi stock, cover and bring to a simmer. Cover with a lid, lower the heat if needed to keep it at a low simmer and allow to cook for around 2 hours until meat is tender and will shred easily when pulled from the bones. Turn off the heat.
You can either shred the meat from the bones in the pot, or more easily, take them from the pot and shred on a board/plate. Remove the bones and excess fat and sinew.
Let the broth cool and settle as you are shredding the meat, or ideally a bit longer to allow the fat to rise to the surface. Skim off most of the fat from the top and discard. Return the shredded beef to the broth and warm through.