Turn on your Instant Pot and set to the sauté function for 7 minutes. While it's heating up, pat chicken breasts with paper towels and season with salt and pepper, on both sides. Add the sesame oil to the Instant Pot and then place the chicken breast in, skin side down.
Let the chicken breast cook for about 7 minutes, flipping the chicken halfway through.
Add in the garlic and ginger. Mix around and let cook for about 30 seconds. Your instant pot will be turned off by this point but don't worry, it is still very hot. Pour in the chicken stock and mushroom broth (or miso ginger broth) and the soy sauce and rice wine vinegar.
Place the lid back on and lock and set the timer to manual high pressure for 20 minutes. Make sure the valve is placed in the sealed position. While your instant pot is cooking, make your eggs.
To make the jammy eggs: Bring water to a medium boil in a medium saucepan. Slowly add or lower the eggs into the gentle to medium boiling water, leave for 7 minutes and then immediately remove the eggs and into an ice bath. Wait 3 minutes. To peel: After the eggs have been in the ice bath for a few minutes, lightly tap them on your countertop or a hard surface and peel gently under cold running water. Alternatively, if you have another instant pot, you can make the eggs in your instant pot.
Back to the ramen: After 20 minutes, (make sure all of the pressure has been released before trying to remove the lid.) remove the lid and remove the chicken from the pot and set on a plate or cutting board and shred the chicken using two forks.
Place some zucchini noodles into bowls for serving and ladle some broth into your bowl. The broth is still very hot so will soften the zucchini noodles right away. I personally like my zucchini noodles with a little bite so I don't let them cook for too long. Zucchini noodles that get too soft don't taste that great in my opinion. Alternatively, you can add the zucchini noodles directly into the instant pot insert and let them soften in the broth just for a minute or two.
Top bowls with the cooked shredded chicken, shredded nori, the eggs sliced in half, garnish with scallions and sesame seeds. Enjoy!