Pour the chicken broth into the slow cooker.
In a mixing bowl, combine the white miso paste, soy sauce, sesame oil, garlic, ginger, rice vinegar, brown sugar and chili garlic sauce. Stir together until it is an even consistency.
Whisk the sauce with the chicken broth in the slow cooker.
Add the chicken breasts to the slow cooker and cover. Cook on low for 7-8 hours or on high for 4-5 hours. The chicken should be fall-apart tender.
In the last 30 minutes of cooking, make the eggs by bringing a saucepan full of water to a boil. Cook the eggs for exactly 6 minutes and then immediately place in a bowl full of ice water until they cool. This will give you a jammy yolk. Remove the shell and slice in half.
Turn the slow cooker to the warm setting. Remove the chicken from the broth and shred it with 2 forks into larger pieces.
Add in the ramen noodles, submerging into the broth. Add in the bok choy and mushrooms, allowing them to soften. Place the chicken back in the broth. The dish is ready when the noodles are cooked.
Serve in bowls with the broth, noodles, chicken, bok choy and mushrooms. Top with 2 egg halves, green onions and dollop of chili garlic sauce if you would like.