Parboil and Prep the Ribs: Place the short ribs in a large pot of water and boil for about 10 minutes over medium-high heat. This removes impurities and excess fat. Drain and rinse the ribs under running water, scrubbing off any bone fragments. Cut a few shallow 1/2-inch slits into the meat so it absorbs flavor better during braising.
Make the Sea Kelp Stock: While the ribs are boiling, simmer dried kelp (dashima) in 4 cups of water over medium-low heat for 5 minutes. Remove and discard the kelp. Measure out 2 1/2 cups of the stock to use in the recipe.
Prepare the Braising Sauce: In a blender or food processor, combine onion, pear, kiwi, garlic, soy sauce, brown sugar, rice wine, and 1/2 cup of the kelp stock. Blend until smooth.
Start Braising the Ribs: Place the parboiled ribs in a Dutch oven or heavy pot. Pour the blended sauce over them and add the remaining 2 cups of kelp stock, ginger paste, sesame oil, and pepper. Bring to a boil, then reduce the heat, cover, and simmer for about 1 1/2 hours. Skim off any fat from the surface as it cooks..
Prep and Add the Vegetables: Trim the edges of the carrot and radish pieces if you like — this helps them hold their shape during braising. Score the tops of fresh shiitake mushrooms with a cross pattern for a decorative look. Add the carrots and radishes to the pot and continue simmering for 20–30 minutes, or until the vegetables are tender. If using rehydrated shiitake, add them at this stage.
Finish with Festive Add-Ins: Stir in the fresh shiitake mushrooms, dried jujubes, chestnuts, and ginkgo nuts. Cook for another 10–15 minutes. Remove from heat and let the stew rest for 10 minutes so the flavors meld together.
Serve: Garnish with chopped green onions and sesame seeds. Serve Galbi Jjim warm with rice and kimchi.