Cut, chop, measure all ingredients and have them ready before beginning. The soup comes together quickly. Turn on the sauté function and add the chopped bacon. Cook until mostly done.
Add butter, onion, carrot, celery and bay leaf. Cook, stirring occasionally, for 5 minutes or until onions are just starting to turn translucent.
Add the rosemary, basil, thyme, poultry seasoning, salt, black pepper, and garlic. Cook for about 1 minute stirring frequently. Add the chicken broth and stir. Add the chicken breasts.
Put the lid on and lock in place. Set the stream release knob to the sealing position. Cancel the sauté function.
Press the pressure cook button (Manual) and the + or - to select 9 minutes. It will take several minutes to come to pressure.
When the cooking cycle has ended, let the pot sit undisturbed for 10 minutes (10 minutes natural release). Next turn the steam release knob to venting (in short bursts until you are sure no soup spews out the vent with the steam), and let the remaining pressure out. When the pin in the lid drops down, open the lid.
Remove the chicken breasts to a bowl and discard the bay leaf. Turn on the sauté function again.
Add the gnocchi and stir. Place the glass lid if you have one on the pot. If you placed the pressure cooker's lid on the pot, make sure it is turned to venting.
While the gnocchi is cooking, shred the chicken breasts. Cook the gnocchi until it floats to the top. Just a few minutes.
When the gnocchi is finished, turn off the pot. Add the Parmesan cheese and stir. Add the chicken and then the spinach. Stir. Stir in the heavy cream. Serve hot.