Brown the ground beef: In a large soup pot over medium heat, cook the ground beef until browned and fully cooked, breaking it up as it cooks. Drain excess grease if needed, then transfer the beef to a plate.

Sauté the onion and garlic: In the same pot, melt the butter. Add the diced onion and cook for 3–4 minutes until soft and translucent. Stir in the minced garlic and cook for another 30 seconds until fragrant.

Make the roux: Sprinkle the flour over the onion mixture and stir well for about 1 minute to form a thick paste and cook off the raw flour taste.

Add broth and potatoes: Slowly whisk in the beef broth until smooth. Add the diced potatoes and bring the soup to a gentle boil.

Simmer until tender: Reduce the heat and let the soup simmer for 12–15 minutes, stirring occasionally, until the potatoes are fork-tender.

Stir in milk, cream, and beef: Return the cooked ground beef to the pot. Add the milk and heavy cream, then let the soup simmer gently for 2–3 minutes so the flavors blend together.

Melt in the cheddar cheese: Reduce the heat to low and add the shredded cheddar cheese a handful at a time, stirring continuously until fully melted and smooth.

Season and serve: Taste the soup and season with salt and black pepper as needed. Let it rest for 5 minutes, then ladle into bowls and top with green onions, bacon bits, or extra cheddar if desired.