Preheat the oven to 375°F (190°C). Wash the Yukon Gold potatoes well and slice them into thin, even pieces, about ⅛-inch thick. Set the sliced potatoes aside while preparing the filling.

Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook until browned, breaking it apart with a spoon. Add the diced onion and minced garlic. Cook for another 3–4 minutes, until the onion is soft and fragrant. Season with salt, black pepper, paprika, and Italian seasoning.

Melt the butter in a saucepan over medium heat. Add the flour and stir continuously for about 1 minute. Slowly pour in the milk and heavy cream while whisking to prevent lumps. Continue cooking until the sauce thickens slightly. Season with thyme, salt, and pepper, then remove from the heat.

Lightly grease a baking dish. Arrange a layer of sliced potatoes across the bottom. Add a portion of the seasoned beef mixture, followed by some of the creamy sauce. Repeat the layers until all the potatoes, beef, and sauce have been used.

Sprinkle the shredded cheddar, mozzarella, and grated Parmesan evenly over the top of the casserole.

Cover the baking dish with foil and bake for 45 minutes. Remove the foil and continue baking for another 20–25 minutes, until the potatoes are tender and the cheese is melted, bubbling, and golden.

Allow the casserole to rest for about 10 minutes before serving. Garnish with fresh thyme or parsley and serve warm.