Place the sun dried tomatoes in 2 cups water and set aside. Let soak until softened, approximately 30 minutes, then chop into small pieces. Reserve the soaking liquid and set aside.
Rinse and drain one can of cannellini beans, and puree the other with its liquid in a blender or food processor. Set aside.
Remove heavy cream from the refrigerator and set aside at room temperature until the soup is done cooking. (This will prevent it from curdling when added to the hot soup later).
Add olive oil to Instant Pot and press the “Sauté” button. Set the heat setting to high and add the onion and garlic. Cook, stirring occasionally, until the onion is soft and translucent, approximately 4-5 minutes.
Add chicken broth and scrape any brown bits off the bottom of the container, then add the chopped sun dried tomatoes and soaking liquid, the whole and pureed white beans, mushrooms, cheese rind, and Italian seasoning. Season with salt and black pepper, to taste, and stir to combine.
Submerge the chicken breasts in the liquid and add lid. Securely lock into position and set the pressure value to the “Sealing” position.
Press the “Manual” button and adjust heat setting to high. Then, adjust the cook time to 10 minutes. After a brief pause, the Instant Pot will automatically start building pressure.
When cook time is complete, allow pressure to release naturally for 10 minutes, then flip the pressure value to “Venting” to release any remaining steam.
Carefully open lid and add spinach, arugula, heavy cream, and grated Parmesan cheese. Stir until the greens are wilted and the cheese is completely melted. Taste and adjust seasonings as desired.
Serve immediately with additional grated Parmesan cheese, if desired. Enjoy!