Turn on sauté mode on your Instant Pot and pour in the oil. When hot, add the onion, carrot, and celery. Sauté for 3 minutes. Add the garlic and sauté for 30 seconds. Turn off sauté mode.

Add the flour, salt, and pepper to the pot and whisk it into the oil. Let cook for 30 seconds.

Pour in the chicken broth and whisk to incorporate into the flour mixture.

Place the chicken breasts inside the liquid. Close and lock the lid in place. Press the pressure cook or manual button and set to cook for 8 minutes on high pressure. When done, do a quick release of the pressure.

Remove the lid and transfer the chicken to a cutting board to shred. Once shredded, return it to the pot.

Turn on sauté mode again. When hot, add the gnocchi to the pot and cook until the gnocchi floats to the top, about 3 minutes. Pour in the half and half and spinach. When the spinach is wilted, turn off the pot.