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1
Make the Marinade: Peel the ginger. Remove the skin from the onion, and cut it into quarters. Peel and core the Asian pear, and cut that into quarters, too. Peel the skins from the garlic. Move the ginger, the onion, the pear, the garlic, and the sesame seeds into the bowl of a food processor, and blend until you achieve a smooth-ish paste-you don't need to puree, but you don't want whole pieces of any one ingredient either.
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2
In the base of a medium mixing bowl, whisk together the chili powder, the brown sugar, and the miso paste, until it forms a paste. Add the soy sauce, the mirin, and the sesame oil; whisk. Slice up the scallions, and add them to the bowl too. Finally, add the contents of the food processor. Fold everything together.
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3
Move the short ribs into a large bowl. Massage the marinade into the meat. Move the meat, and any extra marinade, to a large and sealable plastic bag, and then into the fridge. Marinate the meat for at least 4 hours, or overnight.
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4
Braising the Short Ribs: Heat the oven to 250F.
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5
Move the meat and the marinade to a Dutch oven, or another heavy pot with a lid. (If your pot isn't large enough, you can cut the short ribs into pieces with kitchen shears; just feel around the bones. I cut mine into thirds.) Add the beef stock, and stir around the meat, so that the stock incorporates into the marinade. Turn the range to medium-high, and let the stock and marinade come to a simmer. After that, turn off the range, put the lid onto the pot, and move it into the oven. Braise the meat for 2-3 hours, or until the meat is falling off the bone. Check every hour or so. You always want the meat to be half-submerged in liquid during cooking.
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6
When the meat has finished cooking, move the Dutch oven into the fridge, and let it chill for 4 hours, or overnight.
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7
Making the Short Rib Sauce: Mince the shallot. Move it to a small saucepan, along with the brown sugar, the grated ginger (I use a microplane grater; it helps catch the fibers), the sesame seeds, the sriracha, the soy sauce, and the red wine vinegar. Whisk to blend. Turn the heat to medium high, and let the liquid come to a gentle bubble. Cook, stirring occasionally, until the sauce is reduced by 1/3, about 10 minutes. Let the sauce cool.
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8
Whisk in the scallions, sliced, as well as the canola oil. Refrigerate until needed.
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9
Finishing the Short Ribs: When the short ribs have been properly chilled, skim away any solidified fat. Shred the meat from the bones using your fingers; discarding any fat, bone, or gristle.
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10
Empty the short rib sauce into the pot with the shredded short ribs. Heat gently, until the meat is warm and quite moist from soaking up the sauce. Keep the short ribs warm, over very low heat, until you are ready to build the sandwiches.
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11
Make the Slaw and Dressing: Shred the cabbage. Move it to a mixing bowl, and set it aside.
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12
In a small bowl, whisk together the apple cider vinegar, the lemon juice, the white sugar, the mustard, the cayenne, and the sesame oil, until emulsified.
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13
Toss the cabbage with the dressing, until evenly coated. Set the bowl aside.
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14
Building the Sandwiches: When you are ready to serve, cut open each brioche bun. (You can toast them if you like.) Fry the eggs in the canola oil, just until the whites are set and starting to frizzle, but the yolk is still runny. Spoon the warm short rib onto the base of each sandwich, then add a freshly fried egg. Finish with a generous scoop of the slaw.
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15
This is a messy sandwich; embrace it! Slice each sandwich in half, so that the egg runs into the meat and the slaw. Serve immediately.
