In a large pot over medium heat, add olive oil. Once shimmering, add the Italian sausage, breaking it apart with a wooden spoon. Cook for about 6-8 minutes until browned.

Introduce the diced onion to the pot, stirring it into the sausage drippings. Cook for 3-4 minutes until softened. Add minced garlic and sauté for another 30 seconds.

Incorporate diced potatoes and pour in chicken broth. Season with salt, black pepper, and dried thyme. Bring to a boil, then reduce to a simmer for 15-20 minutes.

Once potatoes are tender, gently stir in heavy cream and optional cheddar cheese. Simmer for an additional 5 minutes, being careful not to boil.

Ladle soup into warm bowls, garnishing with fresh parsley or green onions. Serve with crusty bread or garlic flatbread.