Turn on your Instant Pot and set to the sauté function. Pat chicken breast with paper towels and generously 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.
Add the cherry tomatoes. Let the chicken breast and tomatoes cook for about 7 minutes, flipping the chicken halfway through. Some of the tomatoes may begin to burst but that's fine. When finished, remove the chicken breast from the Instant Pot and set aside.
Still on the sauté setting, add in the garlic and ginger. Let cook for about 30 seconds. Pour in the chicken stock and mushroom broth. Add the soy sauce and rice wine vinegar and place the chicken breast back into the Instant Pot.
Place the lid back on and set the timer to manual high pressure for 20 minutes. Make sure the valve is placed in the sealed position. After 20 minutes, (make sure all of the pressure has been released before trying to remove the lid.) remove the chicken and set on a plate. Place dried ramen noodles into the Instant Pot for just a few minutes, into the hot broth. Shred the chicken using two forks.
To serve: using tongs, portion out the ramen noodles into bowls, ladle the broth into each bowl over the noodles. Top with the cooked shredded chicken, shredded nori, the roasted tomatoes, a soft boiled egg, garnish with scallions and sesame seeds. Enjoy!