In a large pot, pour in the olive oil and warm it over medium heat. Once the oil is shimmering, add the finely chopped onion, cooking until it's soft and translucent, about 5 minutes.
Incorporate the minced garlic into the pot with the onions, cooking for an additional minute or until the garlic becomes fragrant.
Raise the heat to medium-high and add the ground beef to the pot. Cook the beef until it's uniformly browned, breaking it apart with a wooden spoon, which should take approximately 5-7 minutes. If there's an excess of fat, drain it carefully.
Add the diced potatoes, beef broth, dried thyme, smoked paprika, and salt and pepper to the mixture. Stir well to combine, then increase the heat and bring the soup to a rolling boil.
Once boiling, lower the heat to a gentle simmer. Cover the pot and let it cook for 15-20 minutes, or until the potatoes are tender and easily pierced with a fork.
After the potatoes are fully cooked, stir in the whole milk and the freshly shredded cheddar cheese. Mix until the cheese is melted and the soup reaches a creamy consistency, ensuring everything is well blended.
Taste the soup and adjust the seasoning with additional salt and pepper if desired.
Ladle the soup into bowls while it's hot, and garnish with freshly chopped parsley for a pop of color and flavor.
Notes
Serve in rustic bowls and consider adding a sprinkle of extra cheese on top before garnishing with parsley.