Preheat your oven to 375°F (190°C). Peel and thinly slice the potatoes to 1/8-inch thickness using a mandoline or sharp knife. Set aside.
Heat butter in a large skillet over medium heat. Add diced onion and cook for 3-4 minutes until translucent. Add minced garlic and thyme, stirring constantly for about 1 minute.
Add ground beef to the skillet and break it apart with a wooden spoon into small crumbles. Cook for 6-8 minutes until no pink remains.
Season the beef with salt, bouillon powder, black pepper, paprika, and oregano. Stir well to combine.
Drain excess grease from the skillet, leaving just a little. Sprinkle flour over the beef and stir until all meat is coated. Cook for 1 minute, stirring constantly.
Pour in beef broth and milk, stirring constantly. Cook for 2-3 minutes until the mixture thickens to gravy consistency that coats the back of a spoon.
Grease a 9x13-inch baking dish with butter or cooking spray. Layer half of the sliced potatoes evenly across the bottom.
Spoon half of the beef mixture over the potatoes and spread evenly. Repeat with remaining potatoes and beef mixture.
Cover the baking dish tightly with aluminum foil. Bake for 45 minutes, or until a knife slides easily through the potatoes.
Carefully remove the foil and sprinkle shredded cheddar cheese evenly over the top. Return to the oven uncovered and bake for 10-15 minutes until cheese is melted and golden.
Remove from oven and let rest for 10 minutes before serving. This allows the sauce to thicken. Garnish with fresh parsley if desired.