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. 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. Increase heat to high and bring 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.
06 - Remove and discard the bay leaf. Stir in the milk or cream and heat gently for 2 to 3 minutes. Season with salt and black pepper to taste.
07 - Ladle hot soup into bowls. Garnish with chopped fresh parsley and grated cheddar cheese if desired.