Preheat the oven to 375°F (190°C).
In a large skillet over medium-high heat, brown the ground beef, sliced sausage, and diced onion, breaking up the beef as it cooks, about 8–10 minutes. Drain excess grease, leaving about 1 tablespoon in the pan.
Stir in the garlic, smoked paprika, garlic powder, onion powder, and Worcestershire sauce. Cook 1 minute until fragrant. Season with salt and pepper and set aside.
In a mixing bowl, whisk together the cream of mushroom soup, beef broth, Worcestershire sauce, and smoked paprika until smooth and pourable.
Arrange half of the sliced potatoes in a slightly overlapping layer across the bottom of a deep 9x13-inch baking dish. Season lightly with salt and pepper.
Spread half of the beef and sausage mixture over the potatoes, then pour half of the gravy evenly over the top.
Repeat with a second layer of potatoes, the remaining meat mixture, and the remaining gravy.
Cover tightly with foil and bake for 45 minutes.
Remove the foil, sprinkle the shredded cheddar evenly over the top, and bake uncovered for 15–20 minutes more, until the cheese is melted and golden at the edges and a fork slides through the potatoes with no resistance.
Let rest for 10 minutes before serving.