Preheat your oven to 375°F (190°C). Grease a 2.5 to 3-quart oval casserole dish with butter or non-stick spray.
In a large skillet over medium-high heat, cook the ground beef, breaking it up with a spoon, until no longer pink. Add the diced onion and cook for 4-5 minutes until softened. Add the minced garlic and cook for 1 more minute. Drain any excess fat.
Reduce the heat to low. Stir in the cream of mushroom soup, milk (or broth), Worcestershire sauce, thyme, paprika, 1 cup of the shredded cheddar cheese, and a generous pinch of salt and pepper. Stir until the cheese is melted and the sauce is smooth and combined.
Arrange half of the thinly sliced potatoes in an even layer on the bottom of the prepared casserole dish. Spoon the entire beef and sauce mixture over the potatoes, spreading it evenly. Top with the remaining potato slices, arranging them neatly or in a slightly overlapping pattern.
Cover the casserole dish tightly with aluminum foil. Bake in the preheated oven for 25 minutes.
Carefully remove the foil. Sprinkle the remaining 1/2 cup of cheddar cheese evenly over the top. Return the dish to the oven, uncovered, and bake for an additional 10-15 minutes, or until the potatoes are fork-tender, the cheese is bubbly and golden, and the edges are lightly browned.
Remove the casserole from the oven and let it rest for 5-10 minutes. This allows the layers to set for cleaner serving. Garnish generously with the chopped fresh parsley before serving.