Place the chicken breasts, whole eggs in shells, ginger, and garlic in a large slow cooker. Cut the tops off the scallions and chop the green ends to use as a garnish later. Tie the white ends with butcher's twine and place in the slow cooker. Pour the chicken broth over the top. Cover the slow cooker and turn on low.
After 2 hours, take one egg out with a pair of tongs. Place in ice water for a couple minutes, then crack the “tester egg” to check the doneness. You want it to be soft-boiled, with firm whites, but soft silky yolk. If the egg is soft-boiled, remove all eggs and place them in a bowl of ice water. If it is close, continue cooking the remaining eggs for another 10-20 minutes, then remove and chill.
Once the eggs are soft-boiled and resting in an ice bath, check that the chicken is cooked through (2 - 2 1/2 hours). Remove the scallions and skim the top of the broth to remove ginger and residue.
Take the chicken out of the broth. Stir in the miso paste. Then add the mushrooms and dried ramen noodles and place the chicken breasts on top to press the noodles down under the broth. Cover and slow cook another 10-15 minutes until the noodles and mushrooms are soft.
To serve, peel the eggs and cut in half. Remove the chicken and slice. Then ladle the ramen noodles and broth into 6 bowls. Place several slices of chicken, some cooked mushrooms, a handful of fresh spinach, and a soft-boiled egg on top of each bowl. Garnish with jalapeños, chopped scallions, toasted sesame seeds, and crushed red pepper.