Pat the chuck roast dry with paper towels. Season generously on all sides with salt and black pepper. Heat oil in a large skillet over medium-high until shimmering. Sear the beef for 4-5 minutes per side until a deep brown crust forms. Transfer to slow cooker.
Reduce heat to medium. Add onion, garlic, and ginger to the same skillet. Cook 4-5 minutes, stirring occasionally, until onion softens and starts to brown at edges. Add tomato paste and cook 1 minute, stirring constantly, until darkened and slightly sticking to pan.
Pour in sake or dry sherry. Scrape up browned bits from the bottom of the skillet with a wooden spoon. Let bubble about 1 minute, then pour entire mixture into slow cooker over beef.
Add beef broth, soy sauce, dried shiitakes, and star anise to the slow cooker. Stir to combine.
Cover and cook on Low for 8 hours or on High for 5 hours, until beef is fall-apart tender.
Remove beef and shiitakes from slow cooker. Strain broth through a fine-mesh strainer into a clean pot or bowl. Discard solids. Whisk miso paste into hot broth until dissolved. Shred beef with two forks, discard large pieces of fat. Return shredded beef to broth.
Bring a separate pot of water to a boil. Cook ramen noodles according to package directions (usually 2-4 minutes). Drain and divide among bowls. For soft-boiled eggs: boil exactly 6 minutes, transfer to ice bath, peel and halve.
Ladle hot broth and beef over noodles. Top with halved soft-boiled egg, sliced scallions, a sheet of nori, and a generous drizzle of chili crisp or sesame oil. Serve immediately.