Heat vegetable oil in a large skillet over medium-high heat. Add the chicken thighs and sear for 3-4 minutes on each side until golden brown. Remove from heat.
In the slow cooker, combine chicken broth, water, minced garlic, grated ginger, soy sauce, miso paste, rice vinegar, and sesame oil. Stir well to dissolve the miso paste.
Place the seared chicken thighs into the slow cooker. Add sliced carrots and shiitake mushrooms.
Cover and cook on low for 6 hours until the chicken is tender and cooked through.
About 30 minutes before serving, carefully remove the chicken thighs from the slow cooker and shred them with two forks. Return the shredded chicken to the slow cooker.
Add dried ramen noodles to the slow cooker and cook for 5-7 minutes until noodles are tender.
Meanwhile, bring a small pot of water to a boil. Gently add the eggs and cook for 7 minutes for soft-boiled eggs. Remove eggs and place in an ice bath to cool. Peel and halve the eggs.
Stir baby spinach leaves into the slow cooker and cook for 1-2 minutes until wilted.
Ladle the ramen broth, noodles, chicken, and vegetables into bowls. Top each bowl with halved soft-boiled eggs, sliced green onions, nori strips, and a sprinkle of toasted sesame seeds.
Serve immediately and enjoy your slow cooker chicken ramen.