In a 2-quart saucepan, heat 1 teaspoon of olive oil over medium-high heat. Add the ground beef, breaking it up with the edge of a spatula, and cook for about 3 minutes, until browned. Drain and remove the beef from the pan, cover, and set aside to keep warm.
In the same pan, heat 1 teaspoon of olive oil. Add the onions, carrots, celery, and salt. Cook, stirring frequently, for about 2 minutes. Add the garlic and cook for 1 more minute.
Sprinkle in the flour, stirring constantly for 1 minute to cook the flour.
Pour in the broth, add the potatoes and the cooked ground beef. Bring the mixture to a boil, then reduce the heat to medium-low. Cover and simmer for 20-25 minutes, until the potatoes are tender, stirring once or twice during cooking.
Stir in the cream, cheese, and pepper. Bring the soup to a gentle boil, stirring frequently, then reduce the heat to low and simmer for 5 minutes, stirring occasionally, until the soup thickens to your liking.
Taste the soup, add additional salt if needed. Pour the soup into a bowl, top with extra shredded cheese and chopped green onions if desired, and enjoy!
Notes
Sauté the vegetables before adding the broth to bring out their natural flavors.
Use sharp cheddar cheese for the best flavor; mild cheese can get lost in the soup.
Cut the potato into small, even cubes to ensure they cook through quickly.
For a thicker soup, simmer a bit longer or use a touch more flour.