Step 1: In a large Dutch oven or heavy-bottomed pot, brown the Italian sausage over medium-high heat, breaking it up with a spoon as it cooks. Once cooked through, remove the sausage with a slotted spoon and set aside, leaving about 1-2 tablespoons of rendered fat in the pot. If needed, add a small drizzle of olive oil.
Step 2: Add the diced onion and minced garlic to the pot. Sauté for 3-5 minutes, until the onion softens and becomes translucent and the garlic is fragrant, being careful not to burn the garlic.
Step 3: Stir in the diced potatoes, carrots, and celery. Cook for another 5-7 minutes, stirring occasionally, allowing the vegetables to slightly soften and absorb the flavors.
Step 4: Pour in the chicken broth, scraping up any browned bits from the bottom of the pot. Stir in the dried thyme, black pepper, and salt. Bring the mixture to a boil, then reduce the heat to a simmer, cover, and cook for 15-20 minutes, or until the potatoes are fork-tender.
Step 5: In a separate bowl, whisk together the whole milk and heavy cream. Gradually stir this creamy mixture into the simmering soup. Continue to simmer gently for another 5-10 minutes, allowing the soup to thicken slightly and the flavors to meld. Do not boil once the dairy has been added.
Step 6: Return the cooked sausage to the pot. Stir in the fresh spinach or kale (if using) and cook until wilted, about 2-3 minutes. Taste the soup and adjust seasonings as needed. Serve hot, garnished with fresh chopped parsley.