01 - Place a large pot over medium heat. Crumble the pork sausage into the pot and cook, stirring occasionally, until browned and cooked through. Drain excess fat if desired.
02 - Add the diced onion, carrots, and celery to the pot with the sausage. Sauté for 4 to 5 minutes, stirring occasionally, until vegetables begin to soften.
03 - Stir in the minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
04 - Add the diced potatoes, dried thyme, bay leaf, and chicken broth to the pot. Increase heat to bring the mixture to a boil, then reduce heat to maintain a gentle simmer.
05 - Cover the pot and simmer for 20 to 25 minutes, or until potatoes are fork-tender when pierced with a knife.
06 - Remove and discard the bay leaf. Stir in the milk or cream and heat gently for 2 to 3 minutes. Taste and adjust seasoning with salt and black pepper as needed.
07 - Ladle hot soup into bowls and garnish with fresh chopped parsley and grated cheddar cheese if desired.