Heat oven to 325ºF (163ºC) with rack set in middle position.
Heat oil in a dutch oven over medium heat until shimmering. Season beef with 2 teaspoons kosher salt. Add half of ribs to pot and sear until golden brown on all side, about 8 minutes.
Transfer ribs to a sheet pan or plate. Repeat browning with remaining ribs. Drain off all but 2 tablespoons grease.
Add onion wedges, 4 sliced cloves garlic and ¼ cup minced ginger to drippings and cook, stirring frequently until onion starts to caramelize, 5–7 minutes.
Stir in 2 cups water, ⅓ cup low-sodium soy sauce, 2 tablespoons gochujang, and 1 ounce chopped dried shiitake mushrooms. Bring to a simmer then nestle ribs back into pot, meat side down, scooping up onions and placing over beef to allow all of the beef to be submerged.
Cover and transfer to oven; braise until beef is tender and easily falls off bone, 3 hours.
Remove pot from oven and gently transfer beef to a sheet pan. Increase oven temperature to 425º (218ºC) and set rack to upper-middle position. In a small bowl whisk together remaining 2 tablespoons gochujang, 3 tablespoons honey, and 3 tablespoons mirin. Brush glaze over ribs then transfer ribs to oven and roast until deeply browned and crisp, about 25 minutes.
Meanwhile, skim fat from pot then stir in 2 cups water, 3 cubed carrots and 1 cubed Daikon, bring to low simmer and cook, partially covered, until carrots are tender, about 15 minutes. Stir in 1 tablespoon mirin and 2 teaspoons rice vinegar; season to taste with additional salt, mirin and vinegar.
When ready to serve, place a bone in a serving bowl and spoon soup over top. Garnish with scallions and sesame seeds.