In a large pot, heat the olive oil over medium heat. Add the chopped onion and cook until soft, about 5 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Increase the heat to medium-high and add the ground beef to the pot. Cook until browned, breaking it apart with a spoon, about 5-7 minutes. Drain excess fat if needed.
Stir in the diced potatoes, beef broth, dried thyme, smoked paprika, salt, and pepper. Bring the mixture to a boil.
Reduce heat to low, cover, and simmer for 15-20 minutes, or until the potatoes are tender.
Once the potatoes are cooked, stir in the milk and shredded cheese. Stir until the cheese has melted and the soup is creamy.