In a large pot or Dutch oven, cook the ground beef over medium heat until browned. Drain off any excess grease.
Add the chopped onion to the pot and cook until softened, about 5 minutes. Add the minced garlic and cook for 1 minute more until fragrant.
Pour in the beef broth, diced potatoes, carrots, and celery. Stir in the salt, pepper, paprika, and thyme.
Bring the soup to a boil, then reduce heat and simmer, covered, for 15-20 minutes, or until the potatoes and carrots are tender.
If you prefer a thicker soup, whisk together the flour and water in a small bowl until smooth. Stir this mixture into the simmering soup and cook for another 2-3 minutes until thickened.
Reduce the heat to low. Stir in the milk and shredded cheddar cheese until the cheese is melted and the soup is creamy. Do not boil after adding the milk and cheese.