Put dried shiitake mushrooms in a bowl and pour boiling water into the bowl to cover the mushrooms. Set aside for about 5 minutes to let them rehydrate.
Separate corn kernels from the cobs. Once the dried shiitake mushrooms are soft and plump, remove them from the liquid and slice the mushroom caps thinly.
Add all ingredients: corn kernels, cobs, chicken breasts, shiitake mushrooms, garlic, chicken stock, 2 1/2 cups of water and salt to the Instant Pot.
Set the Instant Pot to Soup function (don't forget to seal the valve) and cook for 5 minutes on High if releasing pressure naturally, or 6 minutes if using quick release.
Discard the corn cobs. Take the chicken breasts out of the pressure cooker, shred and return to the pressure cooker.
Mix the cornstarch and water to make the cornstarch slurry. Set the Instant Pot to Sauté mode, and when the soup starts to simmer, slowly add the cornstarch slurry and stir to let the soup thicken to your liking.
Add fish sauce (more or less to taste) and plenty of black pepper. Divide into serving bowls, top with scallions and cilantro and serve hot.