Turn the Instant Pot to Sauté mode. Once it reads Hot, add the olive oil.
Add the ground hot Italian sausage and brown it for about 5 to 6 minutes, stirring occasionally.
Add the diced onion, minced garlic, and dried oregano. Stir to combine and cook for 2 to 3 minutes.
Add two cups of chicken broth to deglaze the pot, stirring well.
Add the diced potatoes and pour in the remaining 4 cups of chicken broth. Stir to combine.
Cancel Sauté mode, close the lid, and set the steam release knob to Sealing. Set to Manual for 5 minutes on high pressure.
After the cooking cycle ends, allow a 10-minute Natural Pressure Release, then carefully release any remaining steam.
Open the lid, add the kale, and cover for 2 to 3 minutes to let it soften.
Stir in the heavy cream, and adjust with salt and pepper to taste.
Serve hot, topped with Parmesan cheese.