Sauté Vegetables: Turn on the Instant Pot to the "Sauté" function. Add a drizzle of olive oil and sauté the diced onions, carrots, celery, and minced garlic until they begin to soften, about 3-4 minutes.

Add Chicken: Add the cubed chicken to the Instant Pot and cook until it's no longer pink on the outside, about 3-4 minutes.

Season: Sprinkle the dried thyme or rosemary over the sautéed ingredients and season with salt and pepper to taste.

Pressure Cook: Pour in the chicken broth and add the potato gnocchi. Close the Instant Pot lid and set the valve to the sealing position. Select the "Pressure Cook" or "Manual" mode and set the timer for 5 minutes on high pressure.

Quick Release: Once the cooking cycle is complete, perform a quick pressure release by carefully turning the release valve to the venting position. Wait for the pressure to fully release before opening the lid.

Shred Chicken: Remove the chicken pieces from the pot and shred or dice them into bite-sized chunks.

Add Cream and Greens: Return the shredded chicken to the pot, and pour in the heavy cream or half-and-half. Stir in the chopped spinach or kale. Select the "Sauté" function again and cook for an additional 2-3 minutes, just until the greens are wilted and the soup is heated through.

Adjust Seasoning: Taste the soup and adjust the seasoning with more salt and pepper if needed.

Serve: Ladle the hot Chicken Gnocchi Soup into bowls, garnish with grated Parmesan cheese, and enjoy your delicious homemade meal!