01 - Place a large pot over medium heat. Crumble pork sausage into the pot and cook, stirring occasionally, until browned and cooked through. Drain excess fat if desired.
02 - Add diced onion, carrots, and celery to the pot with the sausage. Cook for 4-5 minutes, stirring occasionally, until vegetables begin to soften.
03 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
04 - Add diced potatoes, dried thyme, bay leaf, and chicken broth. Increase heat to bring to a boil, then reduce to low heat, cover, and simmer for 20-25 minutes until potatoes are fork-tender.
05 - Remove and discard bay leaf. Stir in milk or cream and heat gently for 2-3 minutes without boiling. Taste and adjust seasoning with salt and black pepper as needed.
06 - Ladle hot soup into bowls and garnish with chopped fresh parsley and grated cheddar cheese if desired.