Preheat your oven to 375°F (190°C).
Peel and slice the potatoes thinly and as close to the same thickness as possible so they cook evenly in the casserole.
In a large skillet, melt the butter over medium heat. Add the onion, garlic, and thyme and sauté until the onion is translucent and garlic fragrant.
Add the ground beef to the skillet and cook until browned and cooked through. Break it into small crumbles as it cooks—season with salt, pepper, bouillon powder, oregano, and paprika.
Drain excess fat from the skillet, then sprinkle the flour over the beef mixture. Stir well to combine, and cook for another minute to toast the flour.
Gradually add the beef broth and milk to the skillet, stirring constantly. Continue cooking until the mixture thickens slightly, forming a gravy-like consistency.
Grease your baking dish with butter (or non-stick spray). Then, arrange half of the sliced potatoes along the bottom, followed by half of the ground beef mixture. Repeat with the remaining potatoes and beef mixture.
Cover with foil and bake for about 45 minutes or until the potatoes are tender.
Uncover the dish, sprinkle the shredded cheddar cheese evenly over the top, and bake for another 10-15 minutes or until the cheese melts and bubbles.
Remove from the oven and let it cool for a few minutes. Garnish with fresh parsley and serve.