01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish.
02 - Heat olive oil in a large skillet over medium heat. Sauté chopped onion until translucent, about 3 minutes. Add garlic and cook for 1 minute.
03 - Add ground beef, breaking it up while cooking until browned. Drain excess fat. Season with salt, pepper, and thyme. Remove from heat.
04 - In a small saucepan, melt 2 tbsp beef drippings or olive oil over medium heat. Stir in flour and cook for 1 minute. Gradually whisk in beef broth and milk, stirring until thickened, about 3 to 4 minutes. Remove from heat.
05 - Arrange half of the sliced potatoes in the baking dish. Top with half the beef mixture, then half the sauce. Repeat layers with remaining potatoes, beef, and sauce.
06 - Sprinkle shredded cheddar cheese and paprika evenly over the top layer.
07 - Cover with foil and bake for 45 minutes. Remove foil and bake an additional 15 minutes until potatoes are tender and top is golden brown.
08 - Allow casserole to rest for 10 minutes before serving.