Preheat your oven to 375 degrees F (190 degrees C).

In a large oven-safe skillet or Dutch oven, cook the ground beef over medium-high heat until browned, about 5 minutes. Transfer the beef to a plate, leaving a little fat in the pan for flavor.

In the same pan, add the diced onions, carrots, and celery. Cook for 4 minutes until softened. Then add the minced garlic and cook for another 30 seconds until fragrant.

Add the butter to the pan. Let it melt, then sprinkle in the flour. Whisk constantly for 1 minute to create a roux.

Slowly pour in the milk and beef broth while whisking. Continue whisking until the sauce thickens, about 3 minutes. Then stir in the paprika, thyme, oregano, Worcestershire sauce, salt, and pepper. Taste and adjust seasoning as needed.

Return the beef to the pan. Layer the thinly sliced potatoes on top, then sprinkle the shredded cheese evenly over the potatoes. Press the potatoes gently into the sauce.

Cover the pan with a lid or foil and bake for 35 minutes. Then remove the cover and bake for another 10 minutes until the cheese is golden and bubbly.

Let the casserole sit for 5 minutes before serving. This helps it set. Serve with a big spoon and enjoy the layers of tender potato and creamy beef.