In a large pot over medium heat, add a splash of olive oil and let it heat for about a minute. Add the Italian sausage, breaking it apart with a wooden spoon, and cook until browned, approximately 5-7 minutes. Stir in the diced onion and minced garlic, cooking until the onion becomes translucent and fragrant, about 3-4 minutes.

Next, add the chopped potatoes to the pot along with your choice of chicken or vegetable broth, ensuring the liquid covers the potatoes. Bring the mixture to a rolling boil over high heat. Once boiling, reduce the heat to low, cover the pot, and let it simmer for 15-20 minutes, or until the potatoes are fork-tender, stirring occasionally.

Once the potatoes are softened, gently stir in the cream, allowing it to meld with the broth for that creamy texture. If you're using greens like spinach or kale, toss them in at this point, and heat everything gently on low for about 5 minutes until the greens wilt and the soup is warmed through.

Before serving, taste your Sausage Potato Soup and add salt and pepper to enhance the flavors. Adjust the seasoning according to your preference, making sure each bowl is just right.