1. Cook the Beef: Heat a large Dutch oven or heavy soup pot over medium-high heat. Add ground beef. Break it up with a wooden spoon and season generously with the garlic powder, smoked paprika, salt, and pepper. Cook until browned and crispy in spots. Remove beef with a slotted spoon to a paper towel-lined plate to drain. Leave about 1 tablespoon of rendered fat in the pot.

2. Create the Roux: Reduce heat to medium. Add the butter to the reserved beef fat in the pot. Add diced onion and sauté for 5-7 minutes until soft. Add minced garlic and cook for 1 more minute. Sprinkle the flour over the vegetables and stir constantly for 2 minutes to cook out the raw flour taste.

3. Simmer the Potatoes: Slowly whisk in the broth a little at a time to prevent lumps. Add the peeled, cubed potatoes. Increase heat to bring the pot to a boil, then immediately reduce heat to low, cover, and simmer for 15-20 minutes, or until potatoes are tender when pierced with a fork.

4. Cream and Mash: Stir in the whole milk and heavy cream. Let it heat through gently (do not let it come to a rolling boil). Turn off the heat. Stir in half (1 cup) of the grated cheddar cheese until melted into the base. Using a potato masher right inside the pot, mash about 50% of the potatoes to thicken the broth, leaving the rest in chunks for texture.

5. Season and Assemble: Taste the soup. It will likely need a good amount of salt and lots of freshly cracked black pepper. Ladle the hot soup into serving bowls. Top generously with the reserved crispy ground beef, the remaining shredded cheddar cheese, and sliced green onions. Serve immediately.