Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, cook the ground beef, diced onion, and minced garlic until the beef is browned and the onion is soft, about 7-8 minutes.
Drain excess fat from the skillet. Season the beef mixture with salt, black pepper, and paprika. Stir well and remove from heat.
In a medium bowl, combine the sour cream, milk, and melted butter. Mix until smooth.
Lightly grease a 9×13 inch casserole dish. Spread half of the sliced potatoes evenly on the bottom of the dish.
Layer half of the cooked ground beef mixture over the potatoes.
Spread half of the sour cream mixture over the beef layer.
Sprinkle half of the shredded cheddar cheese over the sour cream layer.
Repeat the layers with the remaining potatoes, ground beef mixture, sour cream mixture, and cheddar cheese.
Cover the casserole dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the potatoes are tender and the cheese is golden and bubbly.
Remove from oven and let the casserole rest for 5 minutes before serving.
Garnish with chopped fresh parsley before serving.