Brown the beef: In a large skillet, cook the ground beef over medium heat until browned. Drain excess grease if needed and transfer to the slow cooker.
Sauté onions and garlic: In the same skillet, melt butter and sauté diced onion until soft, about 3–4 minutes. Add garlic and cook another 30 seconds.
Deglaze and transfer: Pour a splash of beef broth into the pan and scrape up the browned bits, then transfer the onion mixture to the slow cooker.
Add the vegetables: Stir in potatoes and carrots. Pour in the rest of the beef broth and add salt, pepper, and thyme.
Slow cook: Cover and cook on low for 6–8 hours, or on high for 3–4 hours, until the vegetables are tender.
Add cream and thicken: In the last 30–60 minutes of cooking, stir in the milk and cream (or cream cheese). For a thicker soup, stir in a cornstarch slurry (1 tablespoon cornstarch mixed with 2 tablespoons cold water).
Taste and season: Taste the soup and adjust seasoning with more salt and pepper as needed.
Garnish and serve: Ladle into bowls, sprinkle with fresh parsley, and serve hot with bread or crackers.