Trim any excess fat from the chicken thighs, season on both sides with salt and pepper and set aside.

Press the "sauté" button on the Instant Pot, heat for about 1-1/2 minutes, then add the olive oil and the onions.

Sauté the onions until lightly browned around the edges, 3 to 4 minutes, then add the garlic and sauté for 1 minute longer.

Add the carrots and celery, season lightly with salt and pepper and continue cooking for 2 minutes.

Cancel the "sauté" function on the Instant Pot and arrange the chicken thighs on top of the vegetables, keeping them in as much of a single layer as possible.

Pour 3 cups of the chicken broth over the chicken and lock the cover onto the Instant Pot.

Use the  "manual" function to set the Instant Pot to cook for 18 minutes at high pressure.

Once the time is up, release the pressure manually by turning the steam valve to the venting position, being careful to keep your hands and face away from the top of the Instant Pot as you do.

Use tongs to transfer the chicken thighs to a cutting board or large platter and add the remaining 2 cups of chicken broth to the Instant Pot.

Switch the Instant Pot from the "keep warm" function to "sauté," bring the broth to a boil and add the pasta. Cook for 5 minutes, stir in the diced tomatoes and escarole and continue cooking until the greens are wilted and the pasta is tender, 4 to 5 minutes longer.

While the pasta cooks, remove the bones from the chicken thighs, shred the meat and as soon as the pasta is done, add it back to the soup.

To serve, ladle the soup into individual bowls, garnish with chopped parsley and top with grated Parmesan cheese.