Brown the 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 beef to a plate.

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

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

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

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

Stir in dairy and beef: Return the cooked beef to the pot. Stir in milk and heavy cream. Simmer gently for 2–3 minutes until warmed through and slightly thickened.

Melt in the cheese: Reduce heat to low. Add shredded cheddar a handful at a time, stirring until fully melted and smooth before adding more.

Season and serve: Taste and adjust with salt and black pepper. Let rest 5 minutes, then ladle into bowls and add toppings if desired.