Set the instant pot to Saute and heat the oil.
Add chopped onion. Saute until it begins to soften.
Add garlic, carrots and celery. Cook until fragrant, stirring occasionally (approximately 3 minutes).
Season the chicken with salt and Adobo. Place it on top of the vegetables in the pot.
Add 4 cups of the chicken broth.
Close the lid and seal. Pressure cook for 18 minutes. Natural Release.
Pull the chicken out of the pot.
Add the rest of the broth to the pot. Turn the pot to Saute and bring to a boil.
In the meantime, shred the chicken with 2 forks.
When the soup is boiling, add the ditalini. Cook until tender.
Add the chicken back to the pot, along with the pasta sauce.
Add the Parmesan cheese or rind.
Add greens and stir until wilted.
Top with Parmesan cheese if you'd like.