Prep the Potatoes: Dice the peeled potatoes into small, uniform cubes (about 1/2 inch) for even cooking.
Chop the Aromatics: Finely chop the onion and mince the garlic cloves.
Sauté the Aromatics: Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and cook slowly until soft and fragrant (about 4-5 minutes), stirring often.
Brown the Beef: Add ground beef to the skillet, breaking it up with a wooden spoon. Sprinkle in salt, black pepper, dried thyme, and paprika. Cook until the meat is fully browned and no pink remains.
Simmer with Broth: Pour in the beef broth and stir thoroughly. Simmer for 4 minutes to let the flavors meld and reduce slightly. Remove the skillet from the heat.
Combine the Filling: In a large bowl, gently mix the beef mixture with the diced potatoes. Add the sour cream and half of the shredded cheddar. Fold everything together well until the potatoes are evenly coated.
Assemble in Baking Dish: Spoon the mixture into a lightly greased baking dish and spread it out into an even layer. Sprinkle the rest of the shredded cheddar cheese over the top.
Bake: Cover the dish tightly with foil. Bake in a preheated oven at 375°F (190°C) for 30 minutes.
Finish Baking: Remove the foil and return the dish to the oven for another 10-15 minutes until the cheese topping is bubbling and golden brown.
Rest and Serve: Let the casserole rest for 10 minutes before serving. Serve hot, simple, or with a green salad.