In a large soup pot over medium heat, add 1 tablespoon of olive oil. Once the oil is shimmering, crumble the 1 pound of Italian sausage into the pot. Cook, stirring frequently, for about 5–7 minutes until the sausage is browned and fully cooked. If there's excess grease, carefully drain it off.

Introduce the diced onion to the pot, sautéing for 3–4 minutes until it's softened and translucent. Next, stir in the minced garlic and cook for an additional 30 seconds until its fragrant aroma fills your kitchen.

Stir in the diced potatoes, followed by 4 cups of chicken broth. Add ½ teaspoon of salt, ½ teaspoon of black pepper, and ½ teaspoon of dried thyme or Italian seasoning, stirring well to combine. Bring to a gentle boil, then reduce heat to low and simmer uncovered for 15–20 minutes until the potatoes are fork-tender.

Once the potatoes reach that perfect softness, add in 1 cup of heavy cream or half-and-half, along with the optional ½ cup of shredded cheddar cheese. Stir everything together and let it simmer gently for another 5 minutes without boiling.

Ladle the warm Sausage Potato Soup into bowls, sprinkle with chopped fresh parsley or green onions, and serve immediately.