Preheat the oven to 400°F (200°C). Lightly spray a 9x13-inch casserole dish with nonstick cooking spray.
Place the sliced potatoes in a large bowl. Drizzle the melted butter over them and sprinkle with salt. Toss to ensure the potatoes are evenly coated. Arrange the potatoes in the prepared casserole dish, overlapping them as necessary to cover the bottom and sides.
Bake in the preheated oven for 20 to 30 minutes, or until the potatoes are fork-tender.
While the potatoes are baking, heat a large skillet over medium-high heat. Cook the ground beef in the hot skillet, stirring frequently, until browned and crumbly, about 5 to 7 minutes. Drain and discard the excess grease.
Transfer the cooked beef to a large bowl, and add the condensed soup, ¾ cup of the Cheddar cheese, and milk. Season with salt and pepper, then mix everything together until fully combined.
Once the potatoes are done, remove them from the oven. Pour the beef mixture over the potatoes and return the dish to the oven. Bake for an additional 15 minutes, or until the dish is heated through. Sprinkle the remaining Cheddar cheese on top and bake for an additional 4 to 5 minutes, or until the cheese is melted.